Let g(x) be a continuous function and let g(") (x) be the n-th derivative of g(x). Find an example of g(x) such that gm) (x)| < 1 for all n and for all x E R.

Q: Let f (x) = x² – 3. a) Use the definition of derivative to find f' (x).I (Write your answer in the…

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Q: f(x +h) – f(x) lim h f(x) = 3x2 – 10x + 6 1.

A: Given  The function are  1) fx=3x2-10x+6 5) fx=8x    Formula :- f'(x)=limh→0fx+h-fxh .

Q: By the definition of the derivative, the derivative of f(x) = 3x2 is?

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Q: Let F be an anti-derivative of the function x+(1/x)  for x≠0 such that F(−1)=1. If you think that…

A: Suppose F be the anti-derivative of the function x+1x, then Fx=∫x+1xdx

Q: Suppose that f(a) = f(b) = g(a) = g(b) = 0 and the second derivatives of f and g are continuous on…

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Q: Suppose F(t) has the derivative f(t) shown below, and F(0) = 4. Find values for F(1) and F(9) 2 1 -1…

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Q: The graph below shows the derivative of the function y-f(x) on the interval € (0,8). Suppose f(x) is…

A: We have given a graph of a derivative of the function and f(5)=2  With the help of integration we…

Q: h(x) = In (a- 7) (r +3)

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Q: The graph below shows the derivative of the function y=f(x) on the interval € [0, 8]. Suppose f(x)…

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Q: Consider the function H(x): = 23 + 2x - 1 10x + 2 if x > 3 if x < 3 Determine if H is differentiable…

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