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    Calculus : Velocity, Continuity, Limits, Differentiability and Integrability

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    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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    https://brainmass.com/math/calculus-and-analysis/velocity-continuity-limits-differentiability-integrability-18049

    Solution Preview

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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.

    $2.19

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