If f' (r) exists, then lim, r f(x) = f(r)

Q: f(x+Ax)- f(x) Using the first principle of derivative f'(x) = %3D Ax Ax-0 Differentiate: y 4x - 6

A: Derivative of the function

Q: f(x+h) – f(x), Use the definition of the derivative (that is, f'(x) = lim h0 3 = 3r2. dr to show…

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Q: If f(x+y)=f(x)+f(y) for all x , y e R and E(tanx) _ 2f (sinx) f (1) =1,then evaluate lim x’f(sinx)…

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Q: For n 4 we find the derivative of f(x) = x* as follows: f(x + h) - f(x) (x + h)* – x lim f'(x) = lim…

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Q: Q8. We shall formally show that if two functions f and q are both differentiable at c, then we have…

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Q: Find an equation of tangent equation is 2x+6y=3. line to the graph of y=x+lax that is perpendicular…

A: We need to find the equation of the tangent line to the graph y=x+ln(x) that is perpendicular to the…

Q: Let f(x) = 2x² + 1. Use the limit definition of the derivative to find f'(x).

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Q: 20. If f'(r) exists at r= a, then (A) True (B) False lim f(x) = f(a) PTA

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Q: The slope of the tangent line to the graph of the function y = 2x3 at the point (2, 16) is lim2"…

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Q: 2. Given the graph of the function f shown below, determine which of the following statements is…

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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: I feel confident about one of my answers but not sure. Can you help me solve number 1 a-c. Thanks

A: a)Given function is f(x)=x^2+3By defintion , f'(x) can be evaluated as

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: Give two applications of the derivative f(x + h) - f(x) f'(x) = lim h

A: The given function f'x=limh→0f(x+h)-f(x)h is the derivative by first principle.

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

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Q: f'lx) = lim - 2x + 2x %3D (X+Xxj? 2

A: To solve lim∆x→0-2x+2∆x(x+∆x)2, plug in the limit and obtain -2x+2(0)(x+0)2.…

Q: i) f'(2) = 0 and f" (2) < 0 ii) lim-0 16+h)-15) iii) lim, +x f(x) = 2 iv) f(0) = -2 v) lim, 40 f(x)…

A: We can use the concept of function in order to solve the given application of derivative is also…

Q: Use the definition of the derivative (that is, f'(a) = lim sec(x) da to compute h+0

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Q: f(x)-f(7) B) If f'(7) = 5 then find the lim x+7 Vx - V7

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