3. Simplify, and then evaluate using the Direct Substitution Property: lim h→0 (3 + h) 2 − 9 h

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

A:

Q: Suppose that limx→2[f(x)+x2]=α. Find  limx→1(x+1)f(2x) 2α−4 Not applicable  2f(2) 2(α−4)

A:

Q: Q4)A) Find the following limits (for two only). x+1 1. limx→-1 х2-х-2 1-Vx 2. limx→1 1-x 2х 3.…

A: Part 1,Given,           limx→-1x+1x2-x-2

Q: Q1/ Find the following 1. lim + 2 = 3 X00 X 2. lim(5x - 4 + )

A: according to our guidelines we can answer only three subparts, or question and rest can be reposted.…

Q: 25x2 - 70xy + 49y? Find lim by rewriting the fraction first. 5x - 7y (x.y)→(7,5) 5x + 7y 25x2 - 70xy…

A:

Q: Approximate the value of 2x + x lim e" – 1 by substituting in 3 different values of x that get…

A:

Q: A- The result of the follo 2x² + 3x lim xxx³+x+1 02 Oo O 1 O infinity

A: To find: limx→∞2x2+3xx3+x+1

Q: x* – 2x²y + 4y² c) lim x' + 4y² (xyH0,0)

A:

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

A:

Q: Use the L’Hôpital’s Rule following questions. (10 p.) a. Evaluate limx->1 lnx / 2x(2)-3x+1 b.…

A:

Q: V10x – 7y – 10 Find lim by rewriting the fraction first. 10x - 7y – 100 (x,y)→(10,0) 10x - 7y + 100

A:

Q: Q: find lim \-c०s2 2->০

A:

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

A:

Q: Evaluate in terms of the constant a.

A: We have to find the limit in terms of constant a: limx→02a+x This is determinate limit so we need to…

Q: If −x2 − x + 1 ≤ g(x) ≤ x2 − x + 1 for all x does not =0, what is lim x→0 g(x)?

A:

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

A:

Q: ах? + bху + су? y-0 dx + exy + fyx“ ax? + bxy + cy 2. Evaluate lim lim- – lim lim y-0 x0 dx +exy +…

A:

Q: What is the value of c?

A: we have to to find the value of 'c'. limx→c+2x+1=0

Q: If limz - - 19+561 (z² + 38z) = x + iy, what is the value of x - y ?

A:

Q: a. Evaluate limx→5 f(x), where f(x) = { 11x+ (2 +77) Ef x5 f(x) exists.

A: solution is given below..

Q: If f (x) = −x + 8 for x ≤0 and f (x) = 4x + 7 for x > 0, find (a) limx→0+ f (x) (b) limx→0− f (x)

A: We can find the limit as below.

Q: x²+x y-2y lim (x,y)→(4,16) x- Jy

A:

Q: If f(x)=x2−9x−3 , what is limx→3+x2−9x−3 , limx→3−x2−9x−3, and f(3) ?   Is f(x) continuous at 3?

A: Given,              f(x) = x2 − 9x − 3

Q: For f(x) = the square root of 7x+30, how can I find f’(x) using the definition f’(x) = lim as h—>0…

A: Given,          The function is fx=7x+30.We know that,          The derivative of the function is fx…

Q: Q 7 Find lim y+21y2 +71y + 51 y2-9

A: Consider the given limits

Q: EX- Find Lim -im Z-2Z+4 Z-1-13i

A:

Q: If limx→0(2f(x)−15)=45limx→0(2f(x)−15)=45, then what must limx→0f(x)limx→0f(x) equal?

A: Given limx→02fx-15=45 Find limx→0fx

Q: De nty. lim Bx+5 6+X6-

A:

Q: 36. (х, у) —- (0, 0) lim (x + y²) In(x² + y²)

A:

Q: If limz→-14+71i (z² + 28z) = + iy, what is the value of x – y ?

A:

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

A:

Q: If 3x – 2 s f(x) < x² - 3x + 7 for x 2 0, find lim f(x). X3

A: 3x-2≤f(x)≤x2-3x+7

Q: If lim,→-8+11i (z² + 16z) = x + iy, what is the value of x – Y?

A:

Q: Using tables of values, estimate   lim 3x

A:

Q: 18) Find lim f(x) %3D X 2 - A) – B) 2 00 C) 1 D) 4

A: Topic = Limits 18) B

Q: If lim (x approaches 6) (f(x)-4)/(x-3)= 2, how do I find lim (x approaches 6) f(x)?

A: We separate the limit first.

Q: For the lim z (6x +) = 4, find the largest & that "works" for e = 0.0032. (Use decimal notation.…

A: Given,                    We have to find del.

Q: Suppose that limx→ -2 p(x) = 4, limx→ -2 r(x) = 0, andlimx→ -2 s(x) = -3. Find x→ -2 p(x). r(x) .…

A: Suppose that limx→-2p(x) = 4, limx→-2r(x) =0, and limx→-2s(x) =-3.

Q: 1. Using the table of values, estimate lim 3x x-2 а. 3 b. 6 с. 2 d. 5 2. Using the table of values,…

A: Given: L1=limx→23x, L2=limx→1x2+4x-3, L3=limx→2-x3+2x2-3, L4=limx→2+x3+2x2-3 We know that for any…

Q: lim (x,y)→(0,0) x² – y? x2 + xy + y? II

A:

Q: V1+3x-1 lim Answer: 1 %3D

A:

Q: lim 2x + 1 -0

A:

Q: Use l’Hospital's Rule to show that lim 1+ X. = e. コ

A:

Q: use f(x) to find: limx→0f(x), limx→-4f(x), limx→5+f(x), limx→-4-f(x). the discontinuity that is…

A:

Q: f(x) is discontinuous at x=c, then  limx→c-  f(x) ≠ limx→c+ f(x) True or False?

A:

Q: neither x² – 9 A) limx→3 4х — 12 - x2 – 1 - B) limx→1 VI – 1

A:

Q: Using direct substitution, what is lim²+6z_5, Z-2 223 O 1 O 1 O does not exist

A: We have to find    limx→2x2+6x-5x2-3

Q: lim(x,y)->(0,0)  (4x2y)/(x2+y2)1/2

A: Given: lim(x,y)→(0,0)4x2yx2+y2         (1) To compute: The limit.