Let k ER\{0}. Give an example of a function f : R² → R² and c E R² such that lim || f(x) || = k but lim f(x) does not HIC I-C exist.

Q: Let f(x) = 1²-16 +4 1²-16 H-4 x > 0 I≤0 Find lim f(1)

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Q: 3. Let f(2) = if z + 2i, while f(2i) = 3+4i, is f(2) continuous at z = 2i? 2- 2i 4. Evaluate lim (az…

A: 3)Given:

Q: Q:Discuss the continuity of the function f(x) =lim+ sinTt x)" - 1 n- (1+ sinTt x)" +1 at the point x…

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Q: f(x) – f(c) If lim exists, it is called the of f at c.

A: We know, If limx→cf(x)-f(c)x-c,exists it is called the derivative of  f at c.Denoted by f'(c)and f…

Q: |x+1| if x + -1 13. Consider the function f(x) = {x² - 1 Evaluate lim f(x). if x = -1 A) - C) DNE B)…

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Q: 3. Define the function f(x) (a) Evaluate lim f(x) 1+0+ (b) Evaluate lim f(x) I-1 = 2x n+m m x YA m…

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Q: Answer the following True or False: If lim f(x) exists, then f(x) is a differentiable function at x…

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Q: (2) Use the definition of limit of a function to find lim x³-3x-2 x+2x2 - 3x+2

A: To find the limit of the function x3−3x−2x2−3x+2 as x approaches 2, it can apply the definition of…

Q: 1 if x<1 1. Consider the function f(x)= . Evaluate lim f(x). if x 21 2х - 3 C) 0 D) 1 A) 2 В) -1

A: Here we have to use the concept of limit.

Q: 3. Describe the interval(s) on which the function is continuous. c) S(x)= x-1 2, x= 1

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Q: Let f(x) = x3+x. Evaluate lim s→0 (f(x + s) − f(x))/s .

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Q: Let f be a function sati sfying f(x+y)= f(x)f(y)-/4-f(y) for all x, y e R. and lim f(x)= 4. discuss…

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Q: Explain, using limit definition, why f′(x) = 0 for any constant function f(x) = c.

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Q: lim 3i 4 +

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Q: I if X > 4 and J (X). 4X + 1 i1 X<4. Find lim f(x) x→4+

A: Given; f(x)=√x-1 if x&gt;4 and f(x)=x2-4x+1 if x&lt;4.

Q: Which of the following statements about the function y = ƒ(x)graphed here are true, and which are…

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Q: Assume that rs f(x) < 3r. Compute lim f (x)

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Q: Consider the following graph of the function f. X-0 lim f(x) = X→0+ -3 -2 -1 4 3+ True False 2 - + 2…

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