# Calculus : Velocity, Continuity, Limits, Differentiability and Integrability

26) The vertical height in feet of a ball thrown upward from a cliff is given by s(t)=-16t^2+64t+200, where t is measured in seconds. What is the height of the ball, in feet, when its velocity is zero?

27) If the function f is continuous for all real numbers and the limit as h approaches 0 of f(a+h)-f(a)/h = 7 then which statement is true? Please tell why each case is right or wrong and give answer.

a) f(a)=7

b) f is differentialbe at x=a.

c) f is differentiable for all real numbers.

d) f is increasing for x>0.

e) f is increasing for all real differentiable.

25) If f is continuous for all x, which have the same value? Explain.

I. Integral with b on top and a on bottom f(x)dx.

II. Integral with b-a on top and 0 on bottom f(x+a)dx.

III. Integral with b+c on top and a+c on bottom f(x+c)dx.

Answer is I and II only. Tell me why and tell why I is not right.

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26) The verticle height in feet of a ball thrown upward from a cliff is given by s(t)=-16t^2+64t+200, where t is measured in seconds. What is the height of the ball, in feet, when its velocity is zero?

Solution. We first find its velocity, denoted by v(t). Then

So, let .

So,

27)If the function f is continuous for all real ...

#### Solution Summary

Problems involving velocity, continuity, limits, differentiability and integrability are solved and explained in detail.