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study help
mathematics
precalculus

Questions and Answers of Precalculus

Evaluate the indefinite integral. cos(Tt/2) dt
Evaluate the indefinite integral. fre'dx e*dx
Evaluate the indefinite integral. || xVI - x² dx
Evaluate the integral by making the given substitution. | V2t + 1 dt, u= 2t + 1
Evaluate the integral by making the given substitution. х3 и — х* — 5 - dx, x* – 5 5
Evaluate the integral by making the given substitution. sin?0 cos 0 d0, u = sin 0
Evaluate the integral by making the given substitution. и — х3 + 1 |x? ух3 + 1 dx,
Evaluate the integral by making the given substitution. |хе* dx, и — -х? .2
Evaluate the integral by making the given substitution. | cos 2x dx, dx, и — 2х
Lake Lanier in Georgia, USA, is a reservoir created by Buford Dam on the Chattahoochee River. The table shows the rate of inflow of water, in cubic feet per second, as measured every morning at 7:30
If the units for x are feet and the units for a(x) are pounds per foot, what are the units for da/dx? What units does have? a(x) dx
If f (x) is the slope of a trail at a distance of x miles from the start of the trail, what does represent? (x) dx
A honeybee population starts with 100 bees and increases at a rate of n'(t) bees per week. What does represent? (15 100 + n'(t) dt
Use a graph to estimate the x-intercepts of the curve y = 1 - 2x - 5x4. Then use this information to estimate the area of the region that lies under the curve and above the x-axis.
Sketch the region enclosed by the given curves and calculate its area. С Зп/2 | sin x| dx 00
Sketch the region enclosed by the given curves and calculate its area. I,(x – 2|x|) dx
Evaluate the integral. 12x – 1| dx Jo
Evaluate the integral. *1//3 t2 dt 14 – 1
Evaluate the integral. (x – 1)3 dx -2 х
Evaluate the integral. dr rV3/2 1 – r² -2
Evaluate the integral. 10 2e* dx – 10 sinh x + cosh x
Evaluate the integral. (8 2 + t dt .2
Evaluate the integral. (/3 sin 0 + sin 0 tan?0 de sec²0
Evaluate the integral. (7/4 1 + cos²0 de cos'e
Evaluate the integral. 'T/4 sece tan0 do
Evaluate the integral. 10 + 10*) dx Jo
Evaluate the integral.
Evaluate the integral. 2 dx 1
Evaluate the integral. У dy
Evaluate the integral. xp (x + x^)x J
Evaluate the integral. 4 dp 1 + p?
Evaluate the integral. r() 4 + 6u du Vu
Evaluate the integral. r(÷-). 4 dx
Evaluate the integral. (5e* + 3 sin x) dx
Evaluate the integral. (2x – 3)(4x² + 1) dx
Evaluate the integral. (1 + 6w² – 10w*) dw '3
Evaluate the integral. LGr* + t° – 1) đt
Evaluate the integral. ( (4x 3x? + 2x) dx
Evaluate the integral. *3 L (a? – 3) dx -2
Find the general indefinite integral. Illustrate by graphing several members of the family on the same screen S (e* – 2x*) dx
Find the general indefinite integral. Illustrate by graphing several members of the family on the same screen | (cos x + +x) dx
Find the general indefinite integral. sin 2x dx. sin x
Find the general indefinite integral. S2'(1 + 5') dt
Find the general indefinite integral. sec t (sec t + tan f) dt
Find the general indefinite integral. + tan?0) d0 Se | (2
Find the general indefinite integral. + r dr
Find the general indefinite integral. (sin x + sinh x) dx
Find the general indefinite integral. 1 (*+1+ + 1- dx x' + 1
Find the general indefinite integral. 1+ VI + x -dx
Find the general indefinite integral. | (и + 4)(2и + 1) du
Find the general indefinite integral. (u – 2u* – u² + }) du
Find the general indefinite integral. |(5 + 3x² + r) dx
Find the general indefinite integral. SF dx
Find the general indefinite integral. ((x13 + 7x25)dx
Verify by differentiation that the formula is correct. la + bx dx (3bx – 2a)(a + bx)2 + C 15b Sxva
Verify by differentiation that the formula is correct. tanx dx = tan x – x + C
Verify by differentiation that the formula is correct. cos'x dx = }x + sin 2x + C
Verify by differentiation that the formula is correct. V1 + x? xp- 1 xVI + x?
The area labeled B is three times the area labeled A. Express b in terms of a. Ул y= e* х УА y = e* B х
Letand(a) Find an expression for t(x) similar to the one for f (x).(b) Sketch the graphs of f and t.(c) Where is f differentiable? Where is t differentiable? if x
(a) Show that cos (x2) > cos x for 0 < x < 1.(b) Deduce that Sa cos(x?) dx > п/6
(a) Show that1 < √1 + x3 < 1 + x3 for x > 0.(b) Show that 1< ; /1 + x³ dx< 1.25.
If f is continuous and g and h are differentiable functions, find a formula for d ch(x) f(t) dt dx Jg(x)
Evaluate the limit by first recognizing the sum as a Riemann sum for a function defined on [0, 1]. i п Σ п n? i=1
If f (1) = 12, f' is continuous, and what is the value of f(4)? iS'(x) dx = 17,
If find g''(π/6). *sin x f(x) = m* /1 + t² dt and g(y) = { f(x) dx.
Let
Let where f is the function whose graph is shown. Where is F concave downward? F(x) = ff f(t) dt, У –1
If on what interval is f increasing? - f(x) = f (1 1)e dt_ -
Find the derivative of the function. sin x In(1 + 2v) dv y = cos x
Find the derivative of the function. F(x) *2x arctan t dt
Find the derivative of the function. F(x) = | x2 dt х
Find the derivative of the function. t sin t dt g(x) = J1-2x (1+2x Ji-2x
Find the derivative of the function.
What is wrong with the equation? TT x sec?x dx = tan
What is wrong with the equation? 3 •2 4 dx = 2 x2 -1 X -1
What is wrong with the equation? 1. 3 x4 dx -3 -2 8.
Evaluate the integral and interpret it as a difference of areas. Illustrate with a sketch.
Sketch the region enclosed by the given curves and calculate its area. y = 4 - x2, y = 0
Sketch the region enclosed by the given curves and calculate its area. y = x3, y = 0, x = 1
Sketch the region enclosed by the given curves and calculate its area.y = √x, y = 0, x = 4
Evaluate the integral.that f is integrable by Theorem 3 in Section 5.2. if -2 < x
Evaluate the integral. sin x if 0 < x< T/2 cos x if T/2
Evaluate the integral. 4 dx V1 – x? J1/2
Evaluate the integral. | 2° ds
Evaluate the integral. 2y – y *з у y dy
Evaluate the integral. 8. -dx .2 J1/V3 1 + x-
Evaluate the integral. | cosh t dt 0,
Evaluate the integral. | (x° + e*) dx
Evaluate the integral. c18 dz
Evaluate the integral. c2 v³ + 3v° dv v4
Evaluate the integral. '3 (2 sin x – e*) dx
Evaluate the integral. | (1 + r)° dr
Evaluate the integral. *T/3 csc² 0 d0 T/4
Evaluate the integral. T/2 csc t cot t dt T/6
Evaluate the integral. (Зи — 2)(и + 1) da
Evaluate the integral. •4 2 + x² dx ух
Evaluate the integral. [( (4 – 1) Vī dt
Evaluate the integral. [ (и + 2)(и — 3) du
Evaluate the integral. r5 e dx -5

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