If h(x) →5 as x→ 1 and k(x) → 0+ as h(x) k(x) X→ 1 ? x → 1, then what is lim L

Q: If 8 cos (3x) < g(x) < 8 + 2x for all x. Find lim g(x)

A:

Q: 1. Let f(x) = 3² – 2x + 1. Compute lim (x)f – (4 + x)f 0+-4

A:

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: f(x) – f(c) If lim exists, it equals the slope of the х — с to the graph of f at the point (c,…

A: If    limx→cf(x)-f(c)x-c  exists;

Q: 3. Sketch a graph of a function y = f(x) that satisfies all of the following (if possible): а. x-0-…

A:

Q: If g(x) is differentiable at x = 1, then lim g(x) = g(1). x+ 1+ True False

A: A function f(x) is differentiable at x=a, if limit exist at x=a and is equal to f(a)

Q: 7. Use the definition of the limit of a function to show that if lim f(x) = a and lim g(x) = b, x→x0…

A:

Q: Let f(x) = 2/(2 – x) and g(x) = 8/(4 – x²) Find lim [f(x) –- g(x)] 7. a.

A:

Q: 2. Assume all given functions are continuous. If lim (f(x) - g(x)) = 10 and ƒ(5) = -8 x → 5 Find g…

A: The objective of this question is to find the value of g(5) given that the limit as x approaches 5…

Q: If f(x+ y)= f(x)f (y) for all x, y eR and f (x)=1+g(x)G(x), where lim g (x)=0 and lim G (x)…

A: The problem has been solved in detail in the next step.

Q: If a function f(x) is given by x²-2x-8 T²-7x+12' 6, is f(x) continuous at x = 4? = x 4, x = 4, Yes…

A: The given function fx=x2-2x-8x2-7x+12,x≠46,x=4. We have to check whether the function is continuous…

Q: . Let (x2 + 1 f(x) = 1( - 2)² if x> 1 if x<1 (a) Find lim,-I- f(x) and lim,→* f(x). (b) Does lim ,1…

A: Given: For (a),     limx→1- f(x)=limx→1 x2+1=12+1=2 and     limx→1+ f(x)=limx→1 x-22=(-1)2 =1

Q: 2.) If x= 3, lim In(x+h)-In(x)

A:

Q: 3. (a) Differentiate the function f(x) = x2 from first principles.

A:

Q: 52. Let X if x 2 (a) Evaluate each of the following, if it exists. (i) lim g(x) (ii) lim g(x) x→1…

A: Limit exist at x = a If left hand limit = right hand limit lim x→a- g(x) = lim x→a+ g(x)

Q: If 3x – 1 0, find lim f(x). X→3

A: Given query is to find the indicated limit.

Q: 2. Assume all given functions are continuous. If lim (f(x) - g(x)) = 10 and ƒ(5) = -8 x → 5 Find g…

A: The objective of this question is to find the value of g(5) given that the limit as x approaches 5…

Q: 31. If f is continuous and f(3) = 9, which of the following statements must be true? (A) lim f(3x) =…

A: Here we define which statement is true or false.

Q: Suppose f (x) -7x -3x - 8 Evaluate: lim f (x) x→5

A: This is question of limit and continuity Here we have to find limit of function at given value…

Q: 11. Consider the function f(x) = x³-ax²-x+b X+1 lim f(x) exists, determine all value(s) of lim f(x).…

A:

Q: 2. Assume all given functions are continuous. If lim (f(x) - g(x)) = 10 and ƒ(5) = -8 x → 5 Find g…

A: The objective of this question is to find the value of g(5) given that the limit as x approaches 5…

Q: If 3x − 1 ≤ f(x) ≤ x2 − 3x + 8 for x ≥ 0, find lim x→3 f(x).

A: Here we use sandwich theorem Also known as squeeze theoremThis theorem states that , if gx≤fx≤hx in…

Q: If 6 – 4x <g(x)<6 cos x for all x, find lim g(x).

A:

Q: 2f(x) ) lim x→2 g(x)

A: Given: Limit equations is given.

Q: 12. Let L = lim a>0. If L is finite, the (A) a=1 (B) a=2 (C)L- (D) L-

A: We are asked to find a value and L values.

Q: If f(x) = 2[g (x)]³+7, then what is f'(x)? (A) f'(x)=6g (x) g'(x) (B) f'(x)=6g'(x)…

A: Use the chain rule of differentiation and then solve .   As per the bartleby guidelines I am allowed…