Give a pair of functions f: R →R and g : R →R such that g is not tangent to f at 0 and yet lim,0 \f(x)-g(x)| = 0 Illustrate with a sketch.

Q: lim X→0 1 - cos 8x (e³x-1)²

A: Limx-0-1]2

Q: 1) Use the limit definition to find the derivative of the function f(x) = 3x – 5x?. Then find all…

A: Derivative of the function in terms of limit is f'(x)=limh→0f(x+h)-f(x)h

Q: for function f(x) = e=z²/(20²) sketch f(x)!

A: Topic :- Calculus

Q: Please Help For sigmoid function φ ( x ), prove that φ ′ ( x ) = φ ( x ) ( 1 − φ ( x ) )

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Q: Use the definition of a Derivative to show that the function is not differentiable at x = 1. Why is…

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Q: Find the derivative Of 2x² usino efinition of The derivative -SPF pjest W

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Q: Consider the function y=g(x)=-x2+3. Use the limit definition of the derivative to compute a formula…

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Q: BIl f(x)=

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Q: 2) a) Recall that the definition of the derivative of a function f at a point a is given by f(a + h)…

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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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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.