2. 1. 0 -2 -3 -4 [f(x) lim x-1* g(x) lim[f (x) + g(x)] lim[f (x)g(x)] X-2 x-4 on the state the limits. 5. are the of f (x) (on the and g(x) (on the Based

Q: x #2 2 x² – 4 Vx² +1-Va² +1 X-a V3x -3 よ#3 3 x - 3

A: We have to evaluate the given limit.

Q: Vx+4-3 2. a. Find limit lim x-5 (x2-6x+5) 5x + 24 if x < -3 if – 3 < x< 4 if x 2 4 b. If f(x) = x2…

A: We can use L'Hopital rule to solve it.

Q: 2. By drawing a graph illustrate an example of a function f(x) such that it satisfies these three…

A: Topic = Functions

Q: xV1-3x lim | V1-4x3 I-00 %3D

A: Suppose L is limit value of given Limt

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

A:

Q: 5. The graph of f (x) is shown below. y (a) lim f(x)= X-1 (b)lim f (x)= (c)lim f(x)= X-1

A: Given Graph of fx

Q: 4. Is it possible that there exists some function g(x) and some constant L such that lim g(x) = lim…

A: First we need to understand definition of limit:

Q: n each part below, give an example of a function which satisfies the given criteria. Justify that…

A:

Q: 1. Complete the following based on the graph of f(x). 0 10-8-6-4-2 CO 6 4 2 2 -4 क -8. f(x) e 246 6…

A:

Q: 11. Use the definition of the limit of a function to prove that lim g(x) =- 6 if %3D (16x²-9 4x +3 3…

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: Find lim f(x). X→-6 lim f(x) = X→-6

A: We need to find limx→-6-fx

Q: Consider the graph of y=f (x) 5 3 C -5 -4 -3 -2 -1 10 11 -1 Which of the following is true? (A X--3…

A:

Q: -5나 -4 f(x) -3- 2- 1 2 3 4 5 8 --1 2- --3- Consider this graph of the function f (x). Which of the…

A:

Q: Let g(x) and h(X) be functions with lim g (x) = G and lim h (x) = Hwhere G and H are real numbers.…

A:

Q: 13. Sketch the graph of f (x) = }" Sx² + 1 if x -1 and use it to evaluate lim_ ƒ (x) and X→-1- lim…

A: Given that: f(x)=x2+1    if    x≤-13            if     x&gt;-1

Q: Given the function f(x) = Which f the following is/are true? (x- 1)(x + 1) 1. lim f(x) = +00 2-1+ 2.…

A:

Q: (込) 6. (d) lim x→3x-3 x² -9

A: Find the limit . Of [1/(x-3) -6/(x2-9)] when x tends to 3

Q: Expand the function p (z + h) as follows. p (z + h) = V(w+h)²–1 Substitute the function p (z + h) in…

A: They are solving derivative for v=1w2-1

Q: Let f(x) = x² - 4x-21 X-7 Find a) lim f(x), b) lim f(x), and c) lim f(x). X→7 X-0 X→-3

A:

Q: lim f(x) = 8 lim f(x) = -4 f(-6) = 5 I→-6- z-6+ lim f(x) = 2 lim f(x) = 8 f(5) = 4 z+5+ lim g(x) = 6…

A: Given  functions f(x) and g(x)

Q: Use the 8 and € approach like we did in our class to prove the following lim (3x²-5) = -2, Assume 8…

A:

Q: x²-1 if x < -1 -2 if x ≥ - 1 lim g(x), where g(x) = x+1 x-

A: Steps:

Q: 24. Below is the graph of f(x) lim f(x) = x-1 f(-1)=

A: