Find the derivative using the limit definition. f (x) = x? + 5 f(x + h) – f(x) lim h h→0 lim (a + h)² + 5 – (2)² – 5 h lim h→0 lim (z + h)² – (2)² h h→0 (x² + h +5) – (x)² + 5 lim h h→0

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A: We have to find

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Q: Express the limit as a derivative.

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Q: 1 Using the definition of the derivative as a limit, find f'(x) for f(x) x + 1 ||

A: Given that:

Q: 6) Find the derivative f'(x) using the limit definition for f(x)=√x-3 lim Ax→0 f(x + Ax) = f(x) Ax

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Q: 28. Use the limit definition, lim 7 (x+h)- f(x) to determine the derivative of x-1. [Value of 4] h0

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Q: Show work to find the derivative of the function using the limit definition of derivative. g(t) = 6t

A: solution.

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A: Given,

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Q: 1. Cousider the funetion f(r) a- 1. (n) Find /'(r) using the limit definition of the derivative.

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Q: x4/7 – 1 lim f'(a) where x→-1 x + 1 f(x) = and a = x4/7 lim x + 1 1 х>-1 II

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Q: 6) Find the derivative f'(x) using the limit definition for f(x)=√x - 3 lim Ax→0 f(x + Ax) = f(x) Ax

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Q: Find the limit of the function along the path y = 2x X-1 lim (x.y)-(0,0) y -1

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Q: x²-q² lim

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: