x²-4 How come lim x-2 x-2 cannot be evaluated using the quotient limit law? How come lim Vx – 2 cannot be evaluated as lim (x – 2) ? x-2 x-2 Where are linear functions continuous?

Q: 1. I. lim f(x) = 1. 1116 II. lim f(x) = 2. 2416+ 2. I. f(-6) = 2. II. f(-6) is undefined. 3. I. lim…

A:

Q: eSx-e-4x Evaluate the limit lim using l'Hôpital's Rule. x-0 In(1+x)

A:

Q: f(-4) =1 and f (0) =0 f '(x)-3 f '(x)> 0 if x0; ƒ "(x)>0 if x<0 lim f (x) =- and lim f(x)=0 lim…

A:

Q: II. INDETERMINATE FORMS: Evaluate the limit by employing Theorem 23. f(x) F(x) f'(x) F'(x) lim = lim…

A: To evaluate the given limit of the function.

Q: 4-x V6-5x+x f(x) = 1- find the domain 2- find lim f(x), lim f(x), lim f(x) x2 x-2 x-+2

A: givenf(x)=4-x2x2-5x+6solving x2-5x+6 by factorization method=x2-2x-3x+6=x(x-2)-3(x-2)=(x-2)(x-3)and…

Q: X - iy Discuss the limit Lim I+0 X-1y y-0

A:

Q: [3 - x , x 2 a) Find lim f(x) and lim X-2- f(x) X-2+ b)Dose lim f(x) exist ? why? X-2

A:

Q: (5х-4, E If f(x) = 0<x <1 show that lim f(x) exists. %3D 4x - 3x, 1<x<2

A:

Q: 6- (a) lim f(x) x--2 (e) f(x) lim x-3- (b) lim f(x) X-2+ (f) lim f(x) lim, f(x) X3+ (c)

A: According to our terms and conditions I have solved first 3 parts for remaining part repost

Q: x2-4 lim %3D 3. Find the limit (if it exists). X2 x-2

A:

Q: 4 (11) lim f(x) = X-0 (12) lim f(x): %3D |-10 -8 -6 -4 4 8 10 X +0 -2 -4

A:

Q: ((x + 3)2;x 1 f(x) = %3D 1. lim f(x) = x--5- 2. x→-5+ lim, f(x) = %3D 3. lim f(x) = %3D x--5 4.…

A:

Q: 1.1 Explain the difference between an accumulation point and a limit. 1.2 If lim a, = x and lim yn =…

A: Solution a: Difference between Accumulation point and Limit point: Since accumulation point is the…

Q: 9.. a) Ax)= 2x +x Analyze the following limits: lim f (x), lim f(x), lim f(x), x-1 lím f (x) Based…

A:

Q: Calculate the limit: lim(2x – 6x +1) Prove lim(3x – 2)=7. (Hint: Use the & – e definition of the…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: f(x+2)-(3) . f'(3) = lim is 1. n-3 x-1 . f'(1) = lim f(4x+1)-(5) is 4. n-1 x-1 , f'(1) = lim…

A: Ghj

Q: -2 (a) lim h(x) X--3 (b) lim h(x) x--3+ lim h(x) x- -3 (d) h(-3) (e) lim h(x) X- 0 1 lim h(x) x- 0+…

A:

Q: 1+t-V1-t lim

A: To evaluate: limt→01+t-1-tt   if we substitute t=0, we get 00 (indeterminate form)   Consider…

Q: 2.x2 – 3 x 1 Enter DNE if the limit does not exist. a) lim f(x)= r--1- -) lim f(x) = 2+-1+ -) lim…

A:

Q: 3.) lim f (x); f (x) ={-4+ x, x> 3 x-3 limit from the left f(x) limit from the right f(x) 4 2.9 3.5…

A:

Q: x2-25 Find the limit or say is does not exist (show supporting work): lim X-5 3x-15

A: Given, limx→5x2 -253x-15   We have to find the limit

Q: 3 - 2x? +x- 2 Use L'Hopital's Rule to evaluate Support your answer graphically. lim X2 x² +x-6

A: To find: The limit by L'Hopital rule. Given information limx→2x3-2x2+x-2x2+x-6

Q: eim 2メー5 メ4 -2 z lim Vx+4-1-x-2 メ→ メ+3 lim 2-X Z-メ 24メ

A: You have posted multiple questions. As per the instruction, we will be answering only the first…

Q: x- t00 x2 25 x2 = lim x - to (x2 – 25)/x² lim = lim x → t0 x2 - 25 25/x2 1 %3D II

A: In this question we will use basic of calculus i.e concept of limits. As given in question that we…

Q: 9- 9 – x+ z* lim (1) *→2 x-2 x +x-6 lim . X00 (2) x-2

A:

Q: Ise limit notation to describe the unbounded behavior of the given function as x approaches oo and…

A:

Q: 2x - 6 Let f(x) = if x 5 -4x+ 20 Find the following limits: 1. lim f(x) = x-5 2. lim f(x) = x-0…

A:

Q: How do you solve question 14 and 15 ?

A: The given function is,

Q: x 2 x +2 1 Let f(x) = -x x +4 (a) Does lim→-1f(x) exist? If so, what is it? (b) Does lim2 f (x)…

A: * limit exists when left hand limit is equal to right hand limit  at x = a .   * f(x) is continuous…

Q: 5-Vx 4) lim x-25 x-25 5) lim 7-x ל-x ( x² – x3 if x <2 6) Given the function g(x) 15x – 14 if x 2 2…

A:

Q: x2 - 16 - if x>0 x + 4 2) Let f(x) = %3D x2 - 16 - if x<0 X- 4 Find lim f(x). x-0-

A: First I have written the definition of left hand limit , just use this definition for given function…

Q: 49-7 Estimate lim *-7 -7 is approaching to using a table of functional values.

A:

Q: f(x + Ax) - f(x) Find lim Ax-0 Ax f(x) = 3x- 9x %3D Step 1 Find f(x + Ax) by substituting x + Ax in…

A:

Q: 1. (a) Evaluate the limit or state that it does not exist: i. lim 32-1 37-1 ii. lim V1+r-VI-x (b)…

A: The limits are required to be solved. Each part is solved in detail below.

Q: 1/x-1 Evaluate lim does not exist x-0 el/x+1

A:

Q: x - iy Discuss the limit Lim X - iy y0

A:

Q: Q.No 3.) if x<-1 Let f(x)={ax+ B if -13x<1 x² +2 if x21 Find a and B, so that lim f(x) and lim f…

A: Given that, Consider, limx→-1-f(x) = limx→-1- x3 = (-1)3 = -1 limx→-1+f(x) = limx→-1+ (αx+β)=…

Q: - f(x) = -1; lim lim 16. Suppose x-3+ f(x) = -1; and f(-3) is not defined. x-3- Which, if any, of…

A: Given that limx→-3-f(x) =-1 and limx→-3+f(x) =-1. Which implies that limx→-3f(x) =-1. So, Statement…

Q: 2 4x -2 x> - 1 Consider: f(x) = 8x + 8 x< -1 5 x= - 1 Find lim f(x) and lim f(x) and lim f(x) + X→-1…

A:

Q: [3-x x 2 a) Find lim X-2+ f(x) and lim X-2 f(x) b)Dose lim f(x) X-2 exist ? why?

A: We use the definition of the existence of two sided limit to answer the question.

Q: f(4) = f(0) = f(-3) = lim,-2+ f(x) =, limx-2- f (x) = lim,-3+ f(x) = limy-3- f (x) = = limy-4 f(x) =…

A:

Q: x-2 Evaluate: lim Vx-1 - 1 X-2

A: Givrn limit, limx→2x-2x-1-1 is in 00 indeterminate form

Q: lim 1- 4.x 7 +- 3. Compute the limit: x→

A: The given limit is of the indeterminate form 1∞ . To solve the intermediate form of 1∞.…

Q: 4-x lim x-4 5- Vx2+9 a) Evaluate the limit x2+3x+2 b) Discuss the continuity of the function f(x)%3D…

A: We have to find Limit of given rational function and discontinuities of given rational function.

Q: (x³ + 2 x +2 if x2 -1 if x < -1 7. Explain why lim f(x) does not exist for f(x) = {*"* %3D X-1

A:

Q: 13. |z| lim -1 -0.5 -0.01 -0.0001 f(z) 1. 0.5 0.01 0.0001 f(x) What is the value of the value of…

A: Topic- limit

Q: -x + 1,x 2 0 Let f(x) = {x² + sin x -,x <0' (a) Find left-hand and right-hand limits as "x"…

A: Consider the given information:

Q: 6. lim f(x) = +∞, lim f(x) = 0 and f(-1) = -1 %3D x-1- x-1+

A: