Calculus Answers

Choose all expressions that could not be used to find the volume of the box the bump 16 ft 4 ft 3 feet

∫(tan^-1 x)/(1+x² )dx from 0 to 1

If f+g is differentiable at a ,are f and g necessarily differentiable at a?If f.g and f are differentiable at a,what conditions on f imply that g is differentiable at a?

Evaluate the double integral sin(y^3)dA where R is the region enclosed by y=√x , y=2,y=0 .

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y -axis.

y =   3 x ² , y =  0, x =   4

1.  A hollow metal sphere has an outer diameter of 4cm and an inside diameter of 3.85 cm

a.      What is the thickness in cm?

b.     What is the outer volume cm³?

c.      What is the inner volume cm³?

d.     What is the volume of the metal sphere cm³?

lim e7s+2

s→–œ

Differentiate the function or find 𝑑𝑦 𝑑𝑥 and simplify the result.

1. 𝑓(𝑥) = ln(4 + 5𝑥)

2. 𝐹(𝑦) = ln(sin 5𝑦)

3. 𝑦 = ln|𝑥³ + 1|

4. 𝑦 = 𝑥⁵(𝑥+2)/𝑥−3 (by logarithmic differentiation)

5. 𝑦 = 𝑒^5x

6. 𝑦 = 𝑒^x sin 𝑒^x

7. 𝑓(𝑥) = 3^5x

8. 𝑓(𝑥) = 4^sin2x

9. 𝑓(𝑥) = sinh 𝑥²

10. 𝑓(𝑥) = coth 1/x

Find the derivative of y= sinx/2+cotx

discuss the function f(x) = x^4/4 - 3x^2/2 for where mimimum and maximum