Given fx) ={ax + b (2x – 6 if xs -2 if - 2

Q: Find the limits lim х2 — 1 as a. x→1+ b. x→1 c. x→-1+ d. x→-1

A: we have to find the limit    the given expression is

Q: Find the following limits: 3x2 + 8 (a) lim -4x² + 5 x6 – 3x4 – 2 - (b) lim x4 – 3x + 1 -x2 + 2x – 7…

A: The limits can be solved by directly inserting the limits in the function. If the function shows an…

Q: Show that lim (x,y) →(0,0) 16x4 +9y¹2 4x² + 3y6 does not exist.

A:

Q: If || fn-fl|p. os no prove that lim 11 fn V = || f 11 p. له در

A:

Q: x +1 lim Vx2 + 2x +3

A:

Q: Find the limit. 2 – 4x². - 9x + 11 lim - 8x + 6x +2 X00 11 OA. 2 ОВ. оо OC. O D. 1 F/N 8

A:

Q: b* – 1 Show numerically that for b = 2 and b = 4, lim x→0 appears to equal In 2 and In 4,…

A: Given limit:

Q: b* – 1 Show numerically that for b =3 and b = 5, lim appears to equal In 3 and In 5, respectively.

A: Here given

Q: Show that lim (x,y)→(0,0) 16x4+9y12 4x²+3y6 does not exist.

A:

Q: The value of the constant k such that .2 k x +7 lim exits is X - 1 X → 1 7 - 7 -8 -6

A:

Q: Find the limits x2 - 3x + 2 lim x - 4x as a. x→2+ b. x→-2+ c. x→0 d. x→ 1* e. What, if anything, can…

A: We are entitled to answer three sub-parts. Please resubmit the question which you wish to get…

Q: Find the limits x² - 7x lim X-o X + 1

A: Given: limx→∞x2-7xx+1

Q: 1. Prove lim, n+2n³+7 2 0, using the definition.

A: I have used only definition of limit of sequence

Q: If lim, » 1512i (z2 + 30z) = x + iy, what is the value of a

A:

Q: Find lim (√2-t, et-¹, In(t + 1)) t-0

A:

Q: Prove that lim(x,y)→(1,2) (x2 + 2y) = 5 by using the precise definition

A: ε-δ definition: Limit of function f(x,y) at a point (a,b) is 'L' if for every ε>0 there exist…

Q: Find the Limiti lim (xt +2x") メ→ -○

A: Solution is given below

Q: The limit lim (x,y) →(-2,-5) exists and is equal to -20. Select one: O True O False 25x²-4y² 5x-2y

A: The objective of the question is determine the limit existing.

Q: Use the e-d definition to show that lim /a = 2. a-b (Hint: Vā – V6 =

A:

Q: For which value of c does lim -3 exist? You Answered 3 Correct Answer O None of the given choices

A:

Q: 2. Let r > 1. Prove that lim r" = 00,

A:

Q: Determine the limit 2x z 3 lim,> 3z2 1 8x |5 O x=2/3 O x=-5/2 O x=-2/3 O None of the Above

A:

Q: 2x-1 2. lim X-2 \3x+4,

A:

Q: (a) lim V1+ x²

A:

Q: Solve the following limit by definition (ii) lim f (x) = 2 if f(x) : (4 – 2x, x 1 x-1

A:

Q: If 1/(x^2 + 1) ≤ f(x) ≤ 1 + x^2 for all x in the interval (−1, 1), what is lim x→0 f(x)?

A: Please refer the attached image for complete solution.

Q: Use an appropriate definition to prove the following limits. x³ – 16x* = 1 I+0 r°+ 4x² x +2 V9x2 + 4…

A: This is a problem of limit . Based on the formula and concept we will answer the question.

Q: 2. Use Squeeze Theorem to find lim,x f(z), if for all z >4 6e - 15 < {(x) < VI- 2 2e

A:

Q: Suppose that following is true. x2 + 6 if x s 0 if 0 <x < 1 f(x): 7x² - 6 if x 2 1 What is lim f(x),…

A: Just compute right hand limit and left hand limit and see if they are equal or not.

Q: Determine the limit at infinity. 4x -6x2 + 3x lim - -x - 2x+6 O A. 4 OB. OC. 0 D. 4.

A: Given limit is Dividing both numerator and denominator by x^3, we get

Q: A) Find the following limits (for two only). x+1 1. limx-12-x-2 1-V 2. limx-1 1-x 2x 3. limx-0 2x2+x

A: Find the following limits.

Q: 10. lim 2-と is A. -1

A: we have to find the value of the given  limit  lim    x→-∞2-x2x

Q: Q1. Compute the following limits if it exists. √x+2-3. 1-lim( x-7 2-lim (7x²+x+1) x→∞0 4x²+3x

A:

Q: Is it possible to find numbers a, b and c so that an lim n+0o bn3 + cn erists but not equal to 0?…

A: Consider the function:

Q: B. If k is any real number, prove or disprove that sinkx 1. lim x-0 kx = 1.

A: We will prove this by L'Hopital's rule

Q: Calculate the limit algebraically. x² – 12x +35 lim x2 - 5x →5 O -0.4 O-2 -2.4 O 10

A:

Q: Suppose limy-e- f(x) = I and limx-e- g(x) = m. Prove that limxe-(3f (x) + 4g(x)) = 31 + 4m.

A:

Q: Find the limit. 2 )X lim 1+ x4 O A. O О В. 1 O C. 0 O D. 2

A: We have to find

Q: Prove, using the formal definition, that lim,→1- V1– x = 0.

A: Given, limx→1-1-x=0

Q: + 1for all positive x-values, then what is lim f(x)? X+ 4

A:

Q: 13. lim )- (2- x→2 4-x Vx+7-J7 14. lim x→2

A: (13) We have the given limit problem as, limx→22-x4-x On calculating the factors of numerator and…

Q: (b) Find the following limit: 4x +5 lim x+2 2x -1 (i) (ii) lim 4 x+* x* -x' +2

A: The solution is given as

Q: ƒ (₂) If lim fx x-0 = L then which of the following must be true?

A:

Q: The value of the constant k such that x2-kx+7 lim exits is x-1 x+1 -7 7 -8 8 -6

A:

Q: 6. Explain why the limits lim f(x+h) – f(x) and lim f(2) – f(x) h Z-X are each initially in the form…

A: Given that the limits are limh→0fx+h-fxh and limz→xfz-fxz-x.

Q: Let f(x) = x^2 − 10x. If you construct an ϵ-δ proof to show that limx→5 f(x) = −25, what is the…

A:

Q: The value of the constant k such that x²– kx+6 lim exits is X→1 х—1 б -6 -7 7 -8 8.

A: 1). From the given problem:   fx=2x+14   From the power law:   dxndx=nxn-1.   So,…

Q: Find the shown limit.

A: To Determine:  find the limit. Given: we have limx→511x-3x2+1 Explanation: we have a limit…

Q: Given that f(x)={kx2+2,≤22kx,x>2. If limx→2f(x) exist, then k equals.

A: