(a) Find lim f(z), if it exists. -2², f(x) = cos(x), (2-1/2, if # <0 if 0

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

A:

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

A:

Q: Find lim (1 + sin5x) cot3x x-0+

A:

Q: Let f(x) = x² + 3x – 2 f(x) – f(1) a) Find lim x- 1 x+ 1 b) Use your answer in part (a) to find an…

A:

Q: Find the value of the limit lim SINX X 0 2x 02x (a) 0 (b) 1 (c) 1/3 (d) 1/2 (e) 1/4

A: Here we have to find the limit of the function. In the first step use the property of the limit:

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

A:

Q: Let f(x) be a function with all of the following properties. Sketch a graph of y = f(x). Explain…

A: given that the function f(x) is a function with the following properties: a) f(-1)=2, f(1)=1 and…

Q: 3sin(x) lim tan(2x)

A:

Q: If lim f(x) = = co then f (x) XCOS cos² X00

A: Given- If limx→∞fx=∞ then fx=xcos1x To Prove- The above expression.

Q: x² 1) Let f(x): = (Figure 24). Verify the following: x - 1 (a) f(0) is a local max and f(2) a local…

A:

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

A:

Q: You are given two functions, f and g if - 2 1+

A:

Q: (-ト-c)s x-5

A:

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: Consider the function 1– cos(x) f(x): (a) (T) Evaluate lim, →0 f(x) = L. (b) (T) As x → 0, at what…

A: "Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: (x)- f(1) lim f(x) = 2 , where x-1 х-1

A:

Q: b. Determine if the lim f(x) exists, if f(x) is defined as follows: X4 12x + 3, 5x-9, x < 4 x 24…

A: Both question are solved as, follow

Q: b) Let f(x) = x²-1 2-1 ' √x-1 0 < x < 1 1<x<3 2-1 ' 5x+3, 3x Find lim, 1 f(x). 3x-7 c) Let f(x) =…

A: The b part of the question can be solved using the concept of limits.The c part of the question can…

Q: f(r+h)-f(x) 1. Use the definition f (x) = lim to find the first derivative for the function h0 h…

A:

Q: In (2-x) 1-x²-y2¹ (a). Find and sketch the domain of f. 1. Given function f(x, y) = ,do the…

A:

Q: (3) Evaluate lim -(1+sin(4))t dt

A:

Q: x+1-cos²(x) 3sin(x) 7. Find lim

A:

Q: Find the slope of the tangent line to the function’s graph at the given point using the definition…

A:

Q: The product of two numbers x and x + 170 can be simplified to be x + х.

A:

Q: Suppose f(x) and g(x) have the following values: • f(8)= -4 and f'(8)= -6, g(8) 1 and g'(8) = -3. =…

A:

Q: **. (1) lim,- V1+cos 2x 4 (x-) Q3) Find:

A:

Q: If lim x→0 f(x) + x + 1 x sin (3x) = -5, then lim x→0 f(x) + x + 1 x² is equal to

A:

Q: (a) Lim X–1 x +1 -2 X

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Is there a function f such that limx→1 f(x) = 0 and limx→1 f(x) (x-1)³ = -∞?

A: To find:- A function f such that limx→1fx=0 and limx→1 fxx-13=-∞

Q: The graph of f is given. Use the graph to compute the quantities asked for. (If an answer does not…

A:

Q: Find lim f (x) if, for all x, 9 cos (4x) <f (x) < 8x2 +9. lim f (x) = %3D

A: The given inequality is: 9 cos(4x)≤f(x)≤8x2+9