4. Suppose f is differentiable at x = 10- (a) Show that f(xo+h)-f(xo) h f(ro+h)-f(xo - h) (b) Show that 2h lim h→0 lim h→0 : f'(xo). = f'(ro).

Q: Consider the following functions: f(x)=x√3-x; g(x) = x³ - 6x² + 3; h(x)= = ²-9 I² + 1 a) Use the…

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Q: Use the definition of the derivative, f'(x) = lim z+h)-(2) to findf' (x) where f(x) = x³ +1. h→0 O…

A: fx=x3+1

Q: the line 3x+ y=l is the tangent line for the graph of y= f(x) at x=1, then f'(1)= 1 (C) 1 (D) 3 A) 3…

A: The slope of the line y=mx+c is m. The slope is equal to the derivative of y i.e., f'y=m

Q: Use the limit definition of the derivative to show that the derivative does not exist at x = a for…

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Q: Differentiate the function f. Use the form f'(x) = f(x) = 9x² + x + 8 f'(x) = = lim h→0 f(x +h)-f(x)…

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Q: Consider a quadratic function f(x) = ax?+ bx + c, where a, b, CER and a # 0. She hat the tangent…

A: f(x)=ax2+bx+climit definition of derivative states that :f'(x) =limh→0f(x+h)-f(x)hf'(x) =limh→0…

Q: If f. g and h are differentiable functions at a, then f(g+h) is differentiable at a and ( f(g+…

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Q: 26. Determine (a) f(x) = (c) f(x) = where f is continuous. X \x/-3 2x - 1 2x² + 3x - 2 (b) f(x) =…

A: We have to find where function is continuous.First we will find points where function is…

Q: If f' is continuous, f'(2) = 7, and f(2) = 0, then

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Q: Use the four-step definition of the derivative to find f'(x) if f(x) = 5x 4. f(x + h) = f(x + h) –…

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Q: If y = f(x) is a function that is differentiable everywhere, then f(-e) – f(-e – h) f' (-e) = lim ,h…

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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: Suppose that f and g are differentiable functions such that f (0) =2. f'(0) =-5. g (0) =- 3. and…

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Q: if f' is continuous, f(3)=0, and f'(3)=7, evaluate lim x to 0 f(3+5x) + f(3+6x)/x

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Q: d f'(3) using f'(a) = lim 2x² + 3x5 f(a+h)-f(x) h for the following fun

A: Topic:-limit definition of derivatives