2.99 See Answer

Question: Evaluate the definite integral. Fe4e dx/x√


Evaluate the definite integral.
Fe4e dx/x√ ln x,


> Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. 4 + 3 ++ + ...

> Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. 3 – 4 +4 - + ... 16

> (a). Explain the difference between (b). Explain the difference between aj and 内I and E aj

> (a). What is the difference between a sequence and a series? (b). What is a convergent series? What is a divergent series?

> Show that the series is convergent. How many terms of the series do we need to add in order to find the sum to the indicated accuracy? (-1)*+1 (lerror|< 0.00005) A-1

> (a). What is an alternating series? (b). Under what conditions does an alternating series converge? (c). If these conditions are satisfied, what can you say about the remainder after n terms?

> On what interval is the curve y = fx0 t2/t2 + t + 2, dt concave downward?

> If f (x) = fsinxo√1 + t2 dt and g (y) = fy3 f(x) dx, find g"(π/6).

> If f (x) = fx0 (1 – t2) et2 dt, on what interval is f increasing?

> Evaluate the integral. f01 10x dx

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> Evaluate the integral. f1/2√3/2 6/√1 – t2 dt

> find f. f'(x) = √x (6 + 5x) f (1) = 10

> find f. f'(x) = 8x3 + 12x + 3, f (1) = 6

> Find f. f"(x) = 1 - 6x, f (0) = 8

> Find f. f"(x) = 6x + sin x

> Find f. f"(x) = 6x + 12x2

> Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. *cos X y = * (1 + v?)1º dv Jsin x

> Find the antiderivative F of f that satisfies the given condition. Check your answer by comparing the graphs of f and F. f(x) — 4 — 3(1 + х?)-1, F(1) = 0

> Find the antiderivative F of f that satisfies the given condition. Check your answer by comparing the graphs of f and F. f(x) = 5x* – 2x', F(0)=4

> Find the most general antiderivative of the function. (Check your answer by differentiation.) f(x) = 27 + 6 cos x COS %3D

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> Find the most general antiderivative of the function. (Check your answer by differentiation.) f(x) = 3e* + 7 sec?x

> Let S be the solid obtained by rotating the region shown in the figure about the y-axis. Sketch a typical cylindrical shell and find its circumference and height. Use shells to find the volume of S. Do you think this method is preferable to slicing? Expl

> Evaluate the limit by first recognizing the sum as a Riemann sum for a function defined on [0, 1]. 2 3 lim +

> Evaluate the limit by first recognizing the sum as a Riemann sum for a function defined on [0, 1]. lim 4

> The area labeled B is three times the area labeled A. Express a in terms of b. y. y= e" y= e" B A a

> Suppose h is a function such that h (1) = -2, h'(1) = 2, h"(1) = 3, h (2) = 6, h'(2) = 5, h"(2) = 13, and h" is continuous everywhere. Evaluate f21 h"(u) du.

> A manufacturer of corrugated metal roofing wants to produce panels that are 28 in. wide and 2 in. thick by processing flat sheets of metal as shown in the figure. The profile of the roofing takes the shape of a sine wave. Verify that the sine curve has e

> (a). If f is continuous, prove that fπ/20 f (cos x) dx = fπ/20 f (sin x) dx (b). Use part (a) to evaluate fπ/20 cos2 x dx and x fπ/20 sin 2x dx.

> If a and b are positive numbers, show that r(1 – x)* dx = [ x*(1 – x)* dx

> If f is continuous on R, prove that fbaf (x + c) dx = fb+ca+c f (x) dx For the case where f (x) > 0, draw a diagram to interpret this equation geometrically as an equality of areas.

> If f is continuous on R, prove that fbaf (-x) dx = f-1-bf (x) dx For the case where f (x) > 0 and 0 < a < b, draw a diagram to interpret this equation geometrically as an equality of areas.

> If f is continuous and f90 f (x) dx = 4, find f30 xf (x2) dx.

> If f is continuous and f40f (x) dx = 10, find f20f (2x) dx.

> The velocity graph of a car accelerating from rest to a speed of 120 km/hover a period of 30 seconds is shown. Estimate the distance traveled during this period. (km/h) 80 40 10 20 30 (seconds)

> Alabama Instruments Company has set up a production line to manufacture a new calculator. The rate of production of these calculators after weeks is (Notice that production approaches 5000 per week as time goes on, but the initial production is lower b

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> Find the value of the constant C for which the integral converges. Evaluate the integral for this value of C. C 3r + 1) dx x² + 1

> Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 3r u? - 1 du J2x u? + g(x) = Hint: "f(u) du = f(u) du + f* f(u) du /2x

> Find the value of the constant C for which the integral converges. Evaluate the integral for this value of C. 1 C x² + 4 dx X + 2

> Show that f∞0e-x2 dx = f10 √-ln y, dy by interpreting the integrals as areas.

> Show that fπ0x2e-x2 dx = 1/2 f∞0e-x2 dx.

> Estimate the numerical value of f∞0e-x2 dx by writing it as the sum of f40e-x2 dx and f∞4e-x2 dx. Approximate the first integral by using Simpson’s Rule with n = 8 and show that the second integral is smaller than f∞4e-4x dx, which is less than 0.0000001

> Determine how large the number a has to be so that 1 dx < 0.001 x2 + 1

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> As we will see in Section 7.4, a radioactive substance decays exponentially: The mass at time t is m (t) = m (0) ekt, where m (0) is the initial mass and is a negative constant. The mean life M of an atom in the substance is For the radioactive carbon

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> Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. y = sin't dt - :

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> Calculate the moments Mx and My and the center of mass of a lamina with the given density and shape. : p= 2 quarter-circle

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> Sketch the region bounded by the curves, and visually estimate the location of the centroid. Then find the exact coordinates of the centroid. Зх + 2у 3 6, у%3D0, х%3D0

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2.99

See Answer