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

Find the limit or show that it does not exist. lim (e-2* cos x)
Show that f is continuous on (-∞, ∞). |1 – x² if x < 1 if x>1 f(x) Inx
Find f' in terms of g'.f (x) = x2g(x)
Let r(x) = f (g(h(x))), where h(1) = 2, t(2) = 3, h'(1) = 4, t'(2) = 5, and f' (3) − 6. Find r'(1).
Prove that lim Vx esin(7/x) = 0.
Prove that 0. lim x*cos –=
If f and t are the functions whose graphs are shown, letP(x) = f (x) t(x), Q(x) = f (x)/t(x), and C(x) = f (g(x)).Find(a) P'(2),(b) Q'(2), and(c) C'(2). - 1
Find the value of the number a such that the families of curves y = (x + c)-1 and y = a(x + k)1/3 are orthogonal trajectories.
Use continuity to evaluate the limit. lim 3v-2r-4
Find the limit or show that it does not exist. sin'x lim .2 x² + 1 х >00
Determine the infinite limit. lim cot x х
Water temperature affects the growth rate of brook trout. The table shows the amount of weight gained by brook trout after 24 days in various water temperatures.Temperature (°C)
Let t(x) = ecx + f (x) and h(x) = ekx f (x), where f (0) = 3, f' (0) = 5, and f'' (0) = -2.(a) Find t'(0) and t'' (0) in terms of c.(b) In terms of k, find an equation of the tangent line to the
Suppose thatf (1) = 2 f'(1) = 3 f (2) = 1 f' (2) = 2g(1) = 3 g'(1) = 1 g(2) = 1 g' (2) = 4(a) If S(x) = f (x) + g(x), find S'(1).(b) If P(x) = f (x) g(x), find P'(2).(c) If Q(x) = f (x)/g(x), find
The graph of f is given. State, with reasons, the numbers at which f is not differentiable. УА х 6. 4-
(a) For f (x) = x/ln x find each of the following limits.(i)(ii)(iii)(b) Use a table of values to estimate(c) Use the information from parts (a) and (b) to make a rough sketch of the graph of f. lim
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 + 2 if x
Determine the infinite limit. lim (In x² – x-2)|
(a) By differentiating the double-angle formula cos 2x = cos2x - sin2x obtain the double-angle formula for the sine function.(b) By differentiating the addition formula sin (x + a) = sin x cos a +
The graphs of a function f and its derivative f′ are shown. Which is bigger, f′(-1) or f′′(1)? ул
Forfind each of the following limits.(a)(b)(c)(d)(e) Use the information from parts (a)–(d) to make a rough sketch of the graph of f. f(x) In x lim f(x) >00
The graph of f is given. State, with reasons, the numbers at which f is not differentiable. Ул -2 х 4 2.
Suppose that limx→a f (x) = ∞ and limx→a g(x) 5 c, where c is a real number. Prove each statement.(a)(b)(c) lim [f(x) + g(x)] = ∞ lim [f(x)g(x)] = 00 if c > 0
Find the limit, if it exists. If the limit does not exist, explain why. 2 - |x| lim x→-2 2 + x
(a) Find the vertical asymptotes of the function(b) Confirm your answer to part (a) by graphing the function. х? + 1 Зх — 2х2 2.x3
(a) Estimate the value ofby graphing the function(b) Use a table of values of f (x) to guess the value of the limit.(c) Prove that your guess is correct. lim (Vx? + x + 1 + x) X -00 f(x) = Vx? + x +
(a) Use a graph ofto estimate the value of limx→∞ f (x) to one decimal place.(b) Use a table of values of f (x) to estimate the limit to four decimal places.(c) Find the exact value of the limit.
Find the values of a and b that make f continuous everywhere. х* — 4 х — 2 if x< 2 f(x) ах? — bx + 3 if 2
(a) By graphing the function f (x) = (tan 4x)/x and zooming in toward the point where the graph crosses the y-axis, estimate the value of limx→0 f (x).(b) Check your answer in part (a) by
If f (x) = (x - a)(x - b)(x - c), show that f'(x) х — b х— с х — а f(x)
The graphs of a function f and its derivative f′ are shown. Which is bigger, f′(-1) or f′′(1)? УА х
(a) Graph the function f (x) − ex + ln|x - 4| for 0 ≤ x ≤ 5. Do you think the graph is an accurate representation of f?(b) How would you get a graph that represents f better?
If g(x) = √f (x), where the graph of f is shown, evaluate g'(3). У -1
(a) Graph the function f (x) = sin x - 1/1000 sin(1000x) in theWhat slope does the graph appear to have at the origin?(b) Zoom in to the viewing window [-0.4, 0.4] by [-0.25, 0.25] and estimate the
Let H (t) be the daily cost (in dollars) to heat an office building when the outside temperature is t degrees Fahrenheit.(a) What is the meaning of H′ (58)? What are its units?(b) Would you expect
Find the points on the ellipse x2 + 2y2 = 1 where the tangent line has slope 1.
Find the nth derivative of each function by calculating the first few derivatives and observing the pattern that occurs.(a) f (x) = xn (b) f (x) = 1/x
The table shows values of the viral load V(t) in HIV patient 303, measured in RNA copies/mL, t days after ABT-538 treatment was begun.(a) Find the average rate of change of V with respect to t over
Let f and t be the functions in Exercise 63.(a) If F(x) = f ( f (x)), find F'(2).(b) If G(x) = g(g(x)), find G'(3).
Find f'(x). Check that your answer is reasonable by comparing the graphs of f and f'.f (x) = arctan(x2 - x)
Where does the normal line to the parabola y = x2 - 1 at the point (-1, 0) intersect the parabola a second time? Illustrate with a sketch.
(a) If F(x) − f (x) t(x), where f and t have derivatives of all orders, show that F'' = f '' g + 2f'g' + f g''.(b) Find similar formulas for F''' and F (4).(c) Guess a formula for F(n).
If h(x) = √4 + 3f (x), where f (1) = 7 and f'(1) = 4, find h' (1).
Find equations of the tangent line and normal line to the curve at the given point.y = (2 + x)e-x, (0, 2)
Find an equation of the normal line to the curve y = √x that is parallel to the line 2x + y = 1.
Find the derivative of the function. Simplify where possible.y = arctan√1 - x/1 + x
Find equations of the tangent line and normal line to the curve at the given point.x2 + 4xy + y2 = 13, (2, 1)
The biomass B(t) of a fish population is the total mass of the members of the population at time t. It is the product of the number of individuals N(t) in the population and the average mass M(t) of
At what point on the curve y = √1 + 2x is the tangent line perpendicular to the line 6x + 2y = 1?
Find the derivative of the function. Simplify where possible.y = arccos (b + a cos x/a + b cos x), 0 < x < π, a > b > 0
Find equations of both lines that are tangent to the curve y = x3 − 3x2 + 3x − 3 and are parallel to the line 3x − y − 15.
The Michaelis-Menten equation for the enzyme chymotrypsin is v = 0.14[S]/0.015 + [S] Where v is the rate of an enzymatic reaction and [S] is the concentration of a substrate S. Calculate dvydfSg and
Find the derivative of the function. Simplify where possible.y = cos-1(sin-1 t)
Find an equation of the tangent to the curve at the given point.y = x2 - 1 x2 + 1, (0, -1)
Find an equation of the tangent line to the curve y = x4 + 1 that is parallel to the line 32x − y − 15.
A manufacturer produces bolts of a fabric with a fixed width. The quantity q of this fabric (measured in yards) that is sold is a function of the selling price p (in dollars per yard), so we can
Find the derivative of the function. Simplify where possible.y = x sin-1 x + √1 - x2
Find an equation of the tangent to the curve at the given point.y = 4 sin2x, (π/6, 1)
Find an equation of the tangent line to the curve y = x4 + 1 that is parallel to the line 32x - y = 15.
Find the derivative of the function. Simplify where possible.R(t) = arcsin(1/t)
Evaluatelimt→0 t3/tan3 (2t).
For what value of x does the graph of f (x) = ex - 2x have a horizontal tangent?
Use the method of Exercise 55 to compute Q'(0), where
Find R'(0), whereInstead of finding R'(x) first, let f(x) be the numerator and (x) the denominator of R(x) and compute R'(0) from f (0), f g(0), g(0), and g'(0). x - 3x + 5x 1 + 3x + 6x6 + 9x° R(x)
The table shows world average daily oil consumption from 1985 to 2010 measured in thousands of barrels per day.(a) Compute and interpret the average rate of change from 1990 to 2005. What are the
The number N of locations of a popular coffeehouse chain is given in the table. (The numbers of locations as of October 1 are given.)(a) Find the average rate of growth(i) from 2006 to 2008(ii) from
Researchers measured the average blood alcohol concentration C(t) of eight men starting one hour after consumption of 30 mL of ethanol (corresponding to two alcoholic drinks).(a) Find the average
A particle moves along a straight line with equation of motion s = f (t), where s is measured in meters and t in seconds. Find the velocity and the speed when t = 4.f (t) − 10 + 45/t + 1
A particle moves along a straight line with equation of motion s = f (t), where s is measured in meters and t in seconds. Find the velocity and the speed when t = 4.f (t) = 80t - 6t2
Each limit represents the derivative of some function f at some number a. State such an f and a in each case. sin 0 – lim 0>T/6 0 – T/6
Each limit represents the derivative of some function f at some number a. State such an f and a in each case. + 1 cos (T + h) lim
Each limit represents the derivative of some function f at some number a. State such an f and a in each case. 4 х lim 14 х — 4 -|
Each limit represents the derivative of some function f at some number a. State such an f and a in each case. х6 — 64 lim х>2 х — 2
Each limit represents the derivative of some function f at some number a. State such an f and a in each case. e-2+h lim
If 2x ≤ g(x) ≤ x4 + x2 + 2 for all x, evaluate limx → 1 g(x).
Use continuity to evaluate the limit. 5 - x? lim In
Find the limit or show that it does not exist. 2. sin'x lim .2 * x² + 1 >00
Determine the infinite limit. lịm sec x x> (п/2)+ х
The table gives the height as time passes of a typical pine tree grown for lumber at a managed site.Tree age (years) Height
Each limit represents the derivative of some function f at some number a. State such an f and a in each case. 19 + h – 3 lim
Use continuity to evaluate the limit. lim sin(x + sin x)
Find the limit or show that it does not exist. e3x - e-3r lim e 3x + e-3
The table gives the number N(t), measured in thousands, of minimally invasive cosmetic surgery procedures performed in the United States for various years t.t
Find f ′(a).f (x) = 4/√1 - x
Find the limit or show that it does not exist. lim arctan(e*)
Determine the infinite limit. lim In(sin x)
Determine the infinite limit. lim In(x? – 9) x-3+
Use continuity to evaluate the limit. lim x /20 – x²
The unemployment rate U(t) varies with time. The table gives the percentage of unemployed in the US labor force from 2003 to 2012.(a) What is the meaning of U′(t)? What are its units?(b) Construct
Find f ′(a).f (x) = √1 - 2x
Find the limit or show that it does not exist.
Determine the infinite limit. lim (x – 3)5
Find f ′(a).f (x) − x-2
Find the limit or show that it does not exist. lim (x? + 2x') X -00
Determine the infinite limit. 2 — х lim i (х — 1)?
Find f ′(a). 2t + 1 f(t) t + 3
Find the limit or show that it does not exist. lim (e* + 2 cos 3x)
Determine the infinite limit. х+1 lim х35- х — 5
Explain, using Theorems 4, 5, 7, and 9, why the function is continuous at every number in its domain. State the domain. N(r) = tan(1 + e¯)
Find f ′(a).f (t) − 2t3 + t

Showing 25200 - 25300 of 29459

First
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
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