Find the volume?
Find the volume of the solid generated by rotating about the x-axis the region enclosed by the curve y=sec x and the lines x=0, y=0, and x=pi/3. Answer: pi*sqrt(3) Please...
Find the volume of the solid generated by rotating about the x-axis the region enclosed by the curve y=sec x and the lines x=0, y=0, and x=pi/3. Answer: pi*sqrt(3) Please...
The trapezoidal approximation of ∫ sin x dx from 0 to pi using 4 equal subdivisions of the interval of integration is a) pi/2 b) pi c) (pi/4)(1+sqrt(2)) d)...
Let F(x)=∫ sin(t^2) dt from 0 to x for 0≤x≤3. a) Use the Trapezoidal Rule with four equal subdivisions of the closed interval [0, 2] to approximate F(2). b) On what interval...
Find the area enclosed by the curves y=x^3-8x^2+18x-5 and y=x+5. Please show all your work.
If f'(x)=-f(x) and f(1)=1, find f(x). Answer: e^(1-x) Please show all the work.
A region R in the xy-plane is bounded below by the x-axis and above by the polar curve defined by r=4/(1+sin θ) for 0≤θ≤pi. Set up an integral in rectangular coordinates that...
The expression (1/20)(sqrt(1/20)+sqrt(2/20)+sqrt(3/20)+...+sqrt(20/20)) is a Riemann sum approximation for a) ∫ sqrt(x/20) dx from 0 to 1 b) ∫...
Find the integral of (1/2)(4/(1+sin θ))^2 dθ from 0 to pi. Answer: 32/3 Please show all your work.
A particle moves along the graph of y=cos x so that its x-component of acceleration is always 2. At time t=0, the particle is at the point (pi, -1) and the velocity of the particle is <0, 0>...
A polar curve is defined by the equation r=θ+sin2θ for 0≤θ≤pi. a) Find the area bounded by the curve and the x-axis. b) Find the angle θ that corresponds to the point on...
Which of the following is equal to the area of the region inside the polar curve r=2cos(θ) and outside the polar curve r=cos(θ)? a) 3 ∫ cos^2 (θ) dθ from 0 to pi/2 b)...
The point on the curve x^2+2y=0 that is nearest the point (0, -1/2) occurs where y is a) 1/2 b) 0 c) -1/2 d) -1 e) none of the above Answer:...
The area of the closed region bounded by the polar graph of r=sqrt(3+cos theta) is given by the integral a) ∫ sqrt(3+cos theta) d*theta from 0 to 2pi b) ∫...
The Mean Value Theorem guarantees the existence of a special point on the graph of y=sqrt(x) between (0, 0) and (4, 2). What are the coordinates of this point? Answer: (1, 1) Please...
Let f be a function that has derivatives of all orders for all real numbers. Assume that f(3)=1, f'(3)=4, f"(3)=6, and f'''(3)=12. a) Write the third order Taylor polynomial...
Find the asymptotes of the graph of the parametric equations x=1/t, y=t/(t+1). a) x=0, y=0 b) x=0 only c) x=-1, y=0 d) x=-1 only e) x=0, y=1 Please...
A particle starts at time t=0 and moves along the x-axis so that its position at any time t≥0 is given by x(t)=(t-1)^3*(2t-3). a) For what values of t is the velocity of the particle...
A particle moves on the x-axis so that its velocity at any time t≥0 is given by v(t)=12t^2-36t+15. At t=1, the particle is at the origin. a) Find the maximum velocity of the...
Find the radius of convergence of the power series ∑ (-1)^n*(4x+1)^n from n=0 to infinity. Answer: 1/4 I did the ratio test and got limit as n approaches...
Find the radius of convergence of the power series ∑ x^n from n=0 to infinity. Answer: 1 I did the ratio test and got limit as n approaches to infinity of...