Q.Let g : [1,4] –R be continuous function. Define G(x) = L. g(t)dt. Then a. G(x) is differentiable on [1,4] and b. G(x) is differentiable on (1,4) and c. G(x) is differentiable on [1,4] and G = 2xg(x2). d. G(x) is differentiable on (1,4) and G = 2xg(x²). = g(x²). = g(x²). dG dx dG %3D dx dx dx O a O d

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Q: On what domain is the function f(x) = 3 + V5x – 20 continuous?

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Q: 8. Show that the function f(2)= 2 is continuous everywhere but not differentiable anywhere.

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Q: Which of the following functions is differentiable for all values of x? a. fAx) = 2r' + 5x² b.…

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Q: Let esinx SoN f(t) dt and f is a continuous function, determine the value of f ()

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.