All Matches

Solution Library

Expert Answer

Textbooks

Search Textbook questions, tutors and Books

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Tutors
Study Help
Ask a Question
AI Study Help New

Search
Sign In
Register

study help
mathematics
precalculus

Questions and Answers of Precalculus

(a) If t is differentiable, the Reciprocal Rule says thatUse the Quotient Rule to prove the Reciprocal Rule.(b) Use the Reciprocal Rule to differentiate the function in Exercise 16.(c) Use the
Let f(x) = x/√1 - cos 2x.(a) Graph f. What type of discontinuity does it appear to have at 0?(b) Calculate the left and right limits of f at 0. Do these values confirm your answer to part (a)?
Show that the functionis continuous on (-∞, ∞). Jx* sin(1/x) ifx + 0 if x = 0 f(x) =
If a and b are positive numbers, prove that the equationhas at least one solution in the interval (-1, 1). 3 х3 +x — 2 x³ + 2x? – 1
To prove that sine is continuous, we need to show that limxla sin x − sin a for every real number a. By Exercise 63 an equivalent statement is thatUse (6) to show that this is true.Exercise 63Prove
Investigate the family of functionsfn(x) = tanh(n sin x)where n is a positive integer. Describe what happens to the graph of fn when n becomes large.
(a) Prove thatandif these limits exist.(b) Use part (a) and Exercise 65 to find lim f(x) = lim f(1/t) lim f(x) = lim f(1/t)
Evaluate /1 + tan x lim - V1 + sin x .3 x³
Express the limit as a derivative and evaluate. cos 0 – 0.5 lim 0 – T/3 0→ T/3 1/3
Express the limit as a derivative and evaluate. V16 + h – 2 lim
Express the limit as a derivative and evaluate. x17 - lim lim
Evaluate dy if y = x3 - 2x2 + 1, x = 2, and dx = 0.2.
If y = f (u) and u = t(x), where f and t possess third derivatives, find a formula for d3y/dx3 similar to the one given in Exercise 99.
Prove that f is continuous at a if and only if lim f(a + h) = f (a)
A cup of hot chocolate has temperature 80°C in a room kept at 20°C. After half an hour the hot chocolate cools to 60°C.(a) What is the temperature of the chocolate after another half hour?(b) When
Prove, without graphing, that the graph of the function has at least two x-intercepts in the specified interval. y = x? – 3 + 1/x, (0, 2)
For the limitillustrate Definition 9 by finding a value of N that corresponds to M − 100. = 00 lim Vx In x
Cobalt-60 has a half-life of 5.24 years.(a) Find the mass that remains from a 100-mg sample after 20 years.(b) How long would it take for the mass to decay to 1 mg?
For the limitillustrate Definition 8 by finding values of N that correspond to ε − 0.1 and ε − 0.05. 1 - 3x lim Vx² + 1 = 3
Prove, without graphing, that the graph of the function has at least two x-intercepts in the specified interval. y = sin x, (1, 2)
For the limitillustrate Definition 7 by finding values of N that correspond to ε − 0.1 and ε − 0.05. 1 - 3x lim Vx2 + 1 -3
Find the limits as x →∞ and as x →-∞. Use this information, together with intercepts, to give a rough sketch of the graph as in Example 12.y = x2 (x2 - 1)2 (x + 2)
(a) Prove that the equation has at least one real root.(b) Use your graphing device to find the root correct to three decimal places.arctan x = 1 - x
The volume of a right circular cone is V = 1/3π r2h, where r is the radius of the base and h is the height.(a) Find the rate of change of the volume with respect to the height if the radius is
Find the limits as x →∞ and as x →-∞. Use this information, together with intercepts, to give a rough sketch of the graph as in Example 12.y = x3(x + 2) (x - 1)
(a) Prove that the equation has at least one real root.(b) Use your calculator to find an interval of length 0.01 that contains a root. In x = 3 – 2.x
Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. sin x 3D х? — х, (1,2)
A particle moves along a horizontal line so that its coordinate at time t is x = √b2 + c2t2 , t > 0, where b and c are positive constants.(a) Find the velocity and acceleration functions.(b)
Air is being pumped into a spherical weather balloon. At any time t, the volume of the balloon is V(t) and its radius is r(t).(a) What do the derivatives dV/dr and dV/dt represent?(b) Express dV/dt
A particle moves along a straight line with displacement s(t), velocity v(t), and acceleration a(t). Show that a(t) = v(t) dv/dsExplain the difference between the meanings of the derivatives
Find the limits as x →∞ and as x →-∞. Use this information, together with intercepts, to give a rough sketch of the graph as in Example 12.y = x4 - x6
Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. e* — 3 — 2х, (0, 1) it
Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. - Jx, (2, 3) In x = x
Find the limits as x →∞ and as x →-∞. Use this information, together with intercepts, to give a rough sketch of the graph as in Example 12.y = 2x3 - x4
The function C(t) = K(e-at - e-bt), where a, b, and K are positive constants and b > a, is used to model the concentration at time t of a drug injected into the bloodstream.(a) Show that
Prove thatUse lim Vx = Va if a > 0. х x + Ja
Let P and Q be polynomials. Find if the degree of P is (a) Less than the degree of Q and(b) Greater than the degree of Q. P(x) lim Q(x) х-
Sketch the parabolas y = x2 and y = x2 - 2x + 2. Do you think there is a line that is tangent to both curves? If so, find its equation. If not, why not?
In Section 1.4 we modeled the world population from 1900 to 2010 with the exponential functionWhere t = 0 corresponds to the year 1900 and P(t) is measured in millions. According to this model, what
Prove that lim х—2 х
The average blood alcohol concentration (BAC) of eight male subjects was measured after consumption of 15 mL of ethanol (corresponding to one alcoholic drink). The resulting data were modeled by the
Draw a diagram showing two perpendicular lines that intersect on the y-axis and are both tangent to the parabola y = x2. Where do these lines intersect?
Evaluate 1000 х - 1 lim х — 1 х>1
A tangent line is drawn to the hyperbola xy = c at a point P.(a) Show that the midpoint of the line segment cut from this tangent line by the coordinate axes is P.(b) Show that the triangle formed by
(a) Graph the function(b) By calculating values of f (x), give numerical estimates of the limits in part (a).(c) Calculate the exact values of the limits in part (a). Did you get the same value or
Find h' in terms of f' and t'.h(x) = f(t(sin 4x))
Find h' in terms of f' and t'.h(x) = √ f(x)/g(x)
The graph of any quadratic function f (x) − ax2 + bx + c is a parabola. Prove that the average of the slopes of the tangent lines to the parabola at the endpoints of any interval [p, q] equals the
Find h' in terms of f' and t'.h(x) = f (x) t(x) f (x) 1 t(x) 80.
What is the value of c such that the line y = 2x + 3 is tangent to the parabola y = cx2?
Evaluate /6 — х — 2 lim (3 — х — 1 - 2 х—2
Find f' in terms of g'.f(x) = t (ln x)
Find the horizontal and vertical asymptotes of each curve. If you have a graphing device, check your work by graphing the curve and estimating the asymptotes. 2e* e* – 5
Find the horizontal and vertical asymptotes of each curve. If you have a graphing device, check your work by graphing the curve and estimating the asymptotes. х3. — х y = х? — 6х + 5
If prove that limx → 0 f (x) − 0. .2 x? if x is rational if x is irrational F(x) =
If find the following limits.(a)(b) f(x) - 5, lim .2 х* lim f(x)
(a) Show that f (x) = x + ex is one-to-one.(b) What is the value of f-1(1)?(c) Use the formula from Exercise 77(a) to find s f-1)'(1).
If r is a rational function, use Exercise 57 to show that limx → a r(x) − r(a) for every number a in the domain of r.Exercise 57If p is a polynomial, show that limx → a p(x) − p(a).
Find the horizontal and vertical asymptotes of each curve. If you have a graphing device, check your work by graphing the curve and estimating the asymptotes. 1 + x* y .2 - x4
Determine the infinite limit. x csc x lim х>2п
Let P represent the percentage of a city’s electrical power that is produced by solar panels t years after January 1, 2000.(a) What does dP/dt represent in this context?(b) Interpret the statement
Find the value of c such that the line y − 3/2 x + 6 is tangent to the curve y = c√x.
Find the 1000th derivative of f(x) = xe-x.
Let f (x) − [[cos x ]], -π ≤ x ≤ π.(a) Sketch the graph of f.(b) Evaluate each limit, if it exists.(i)(ii)(iii)(iv)(c) For what values of a does limx→xaf(x) exist? lim f(x) х- lim f(x)
Find f' in terms of g'.f(x) = ln |t(x)|
Find f' in terms of g'.f(x) = et(x)
Suppose the curve y = x4 + ax3 + bx2 + cx + d has a tangent line when x − 0 with equation y = 2x + 1 and a tangent line when x = 1 with equation y = 2 - 3x. Find the values of a, b, c, and d.
For what values of r does the function y = erx satisfy the differential equation y'' - 4y' + y = 0?
Find f' in terms of g'.f(x) = g(ex)
Find f' in terms of g'.f(x) = g (g (x)
Find the limit or show that it does not exist. lim [In(2 + x) – In(1 + x)] X 00
The graph of f is given. State, with reasons, the numbers at which f is not differentiable. y. -2 4 х
Let g(x) − sgn(sin x).(a) Find each of the following limits or explain why it does not exist.(i) (ii)(iii)(iv)(v)(vi)(b) For which values of a does limx → a g(x) not exist?(c) Sketch a graph
Where is the function h (x) = |x - 1| + |x + 2| differentiable? Give a formula for h′ and sketch the graphs of h and h′.
If F(x) = f (x f (x f (x))), where f (1) = 2, f (2) = 3, f' (1) = 4, f' (2) = 5, and f' (3) = 6, find F' (1).
Find f' in terms of g'.f(x) = [g(x)]2
Find f' in terms of g'.f(x) = g(x2)
(a) Use implicit differentiation to find y' ifx2 + xy + y2 + 1 = 0(b) Plot the curve in part (a). What do you see? Prove that what you see is correct.(c) In view of part (b), what can you say about
Find the horizontal and vertical asymptotes of each curve. If you have a graphing device, check your work by graphing the curve and estimating the asymptotes. 2x? + x – 1 У х2 +x — 2 х* 2
Suppose f is continuous on [1, 5] and the only solutions of the equation f (x) − 6 are x − 1 and x − 4. If f (2) − 8, explain why f (3) > 6.
Find the horizontal and vertical asymptotes of each curve. If you have a graphing device, check your work by graphing the curve and estimating the asymptotes. 2x² + 1 y = Зx? + 2х — 1
Nick starts jogging and runs faster and faster for 3 mintues, then he walks for 5 minutes. He stops at an intersection for 2 minutes, runs fairly quickly for 5 minutes, then walks for 4 minutes.(a)
Prove that lim In x x→0+ = -0.
Find the limit, if it exists. If the limit does not exist, explain why. 2х — 1 lim х—0.5— |2x³ – x²| х>0.5- |2х3 — х?
Determine the infinite limit. lim Inx
Use the definition of a derivative to find f′(x) and f′(x). Then graph f, f′, and f′′ on a common screen and check to see if your answers are reasonable.f (x) = x3 - 3x
Consider the function (a) Show that(b) Show that(c) What can you conclude about f(x) = tan |f(x) = 0 for x п 2т 3т
Find the horizontal and vertical asymptotes of each curve. If you have a graphing device, check your work by graphing the curve and estimating the asymptotes. 5 + 4x y = x + 3
Determine the infinite limit. x? – 2x – 8 lim x-2+ x? – 5x + 6
Let f (x) = 1/x and g(x) − 1/x2.(a) Find (f° g) (x).(b) Is f° g continuous everywhere? Explain.
Find the numbers at which f is discontinuous. At which of these numbers is f continuous from the right, from the left, or neither? Sketch the graph of f. 2 if x
Find the numbers at which f is discontinuous. At which of these numbers is f continuous from the right, from the left, or neither? Sketch the graph of f. x if x
Find the limit or show that it does not exist. lim [In(1 + x?) – In(1 + x)] X 00
Show that f is continuous on (-∞, ∞). |sin x if x < /4 [ sin f(x) = cos x if x > /4 %3D >T/4
Find the limit or show that it does not exist. lim tan-(In x)
At what numbers is the following function t differentiable?Give a formula for g′ and sketch the graphs of g and g′. 2x if x < 0 if 0 < x < 2 g(x) = {2x – x² if x > 2
Determine the infinite limit. x? – 2x .2 lim x→2- x² – 4x + 4
Suppose N is the number of people in the United States who travel by car to another state for a vacation this year when the average price of gasoline is p dollars per gallon. Do you expect dN/dp to
Find the limit, if it exists. If the limit does not exist, explain why. 2x + 12 lim x→-6 x + 6
If t is a twice differentiable function and f (x) − xg(x2), find f'' in terms of g, g', and g''.

Showing 25100 - 25200 of 29459

First
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
Last

Services

Sitemap
Fun
Definitions
Become Tutor
Study Help Categories
Recent Questions
Expert Questions

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Campus Ambassador

Secure Payment

Download Our App

© 2024 SolutionInn. All Rights Reserved