Let f(x) be a function defined in an open interval containing 'a'. The derivatrive of th on f(x) at 'a', denoted by f'(a) is defined by f'(a) = lim f(ath)-f(a) h→0 h. Provided this limit exists. This is also called Slope (m) of the tangent of function at point (a, f(a)) Example 1. Find the derivative of the following functions at the indicated points. Or Find the Slope of the following functions at the given points. f(x) = x3 7x +3 at x = 1 Solution:

Q: Use the limit definition of the derivative to show that the derivative of the function is Paragraph…

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Q: Let f(x) = (a) f(1) = (b) f'(6) = 2x³ - 5x² x2 Evaluate f'(x) at the following points:

A: f(x)=2x3-5x2x23xba=xbad dx(x)m=mxm-1

Q: Which of these is the limit definition of the derivative of f(x)? O f'(x) f (x + h) – f (x) lim h 00…

A: use the basic definition of derivative to choose the correct option

Q: 1) Use the limit definition of derivative f'(a) = lim h→0 f(a+h)-f(a) h

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Q: Use the limit laws to derive the product rule of derivatives (fg)' = f'g+ fg' by filling in the…

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Q: Suppose f(r) is a function whose Derivative f'(x) is graphed below on the domain [0, 9). y = f'(x) 1…

A: Given: The graph of on the domain . To find: Interval on which is increasing. Interval on which…

Q: Given f(x) = = ƒ'(x)= 3 X " find f'(x) using the limit definition of the derivative.

A: Given , to find  by using the limit definition of the derivative.

Q: Let 1 f(x) = x +3 Use the limit definition of the derivative to find the following. (a) f'(-7) = (b)…

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Q: Let 1 f(x) = X - - 1 A) First calculate f'(a) = lim h→0 f'(a)= (i) ƒ' ( − 2) = = (ii) ƒ'(0) = (iii)…

A: To find the derivative.

Q: 1) Use the limit definition of derivative f'(a) = lim h→0 f(a+h)-f(a) h x to find the equation of…

A: We have to find the equation of the tangent line to the curve y=x1-x at the 0, 0.