Calculus Answers

Use the inequality 5cos(2x)≤0

5cos⁡⁡(2x)≤0 on [−π,π]

[−π,π] to answer the following questions.

Part A: What are the zeros to the nearest hundredth?

Part B: What is the solution set for the inequality?

Select all correct answers for Part A, and select one answer for Part B. Use π≅3.14

π≅3.14 if needed.

A: x= −1/2π

A: x= −3/4π

A: x= 0π

A: x= −1/4π

A: x= 1/4π

A: x= 3/4π

A: x=−1/2π

B: (−3/4π,−1/4π)∪(1/4π,3/4π)

B: [−1/2π,0π]∪[0π,1/2π]

B: [−1/2π,1/2π]

B: [−3/4π,−1/4π]∪[1/4π,3/4π]

B: (−∞,−3/4π]∪[−1/2π,1/2π]∪[3/4π,∞)

1. Use the method of implicit differentiation to determine the derivatives of the following:

a. xsin y + ysin x =1

b. tan(x-y) =y/1+x^2

C. √x+y = x^4 + y^4

d.y + xcos y = x^2 y

2. Find the number "c" that satisfy the Mean Value Theorem (M.V.T) on the given intervals:

a. f(x)= e^-x ; [ 0,2 ]

b. f(x)=x/x+2 ; [ 1, π ]

3.Determine the equation of the tangent and normal at the given points:

a. y + xcos y = x^2 y ; [ 1, π/2 ]

b. h(x) = 2/√x^2 + 1 ; at x=1

The dimensions of a rectangular box are measured to be 75 cm, 60 cm,and 40 cm, and each measurement is correct to within 0.2 cm .Use differentials to estimate the largest possible error when the volume of the box is calculated from these measurements.

For what values of a and b is

g(x)={ax+2b, x<=0

x²+3a-b, 0<x<=2

3x-5, x>2}

continuous at every x?

in triangle ABC, the midpoints of the sides AB, BC and CA respectively. Show that 2AB + 3BC + AC =2LC

Lim_x→1⁺ (³√x+1) In(x+1)

Lim_x→∞ (3cos x / x)

Find the derivative of

y = ln 3x⁵.

[1℄   ln 3x⁵

[2℄   15x⁴

[3℄   5x⁻¹

if the power series is the sum of n=0 to infinity (anx^n) converges uniformly ]alpha,beta[ then so does sum of n=0 to infinity (an(-x^)^n). true or false? justify.

e^x

d/dx [ ∫ ( Int dt] = x- In 2

2

True or false with full explanation