Estimate limr→-4 f (x). Estimate limr→-2 f (x). Where is f(x) discontinuous?

Q: - «) lim (2 – ez x→0

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Q: x-1 numerically. Vx-1 Estimate lim

A: Using rationalization method.

Q: a. limx0 Tn(x) ex+x b. limr-0 2ex+x2 2e*+x2 In(x) c. limx-0+

A: Given; a) limx- infinity x/ln(x) b) limx- infinity (ex+x)/(2ex+x2) c) limx- 0+ln(x)/(1/x).

Q: Q4: A) solve: 1+rsin 1) lim y-0 1+xcos

A: Given: limy→01+xsin1x1+xcos1x

Q: 2.y lim (x.y)-(0.0) 12x- Show that does not exist. -1ly

A: We will show that limx, y→0, 02xy212x2-11y4 doesn't exist. One path: (along x=0)    limx, y→0,…

Q: -xy lim (x,y)→(0,0) x²+y2

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Q: 1-coskx 2. lim kx = 0.

A:

Q: 2) IF f(x) = {" (x + 2 , – 1<x<0 x, 0<x< 1 find limf(x) %3D

A: To find lim(x tends to inf) f(x)

Q: 26. What is the value of lim A. - 2 B. - 1 1-cost t→0 t C.0 D. 1 - ?

A:

Q: lim (х — Vx? + х

A: Consider fx=x-x2+x. Simplify the above function. fx=x-x2+xx+x2+xx+x2+x=x2-x2-xx+x2+x=-xx+x2+x

Q: x4-16y+ lim (x,y)¬(2,1) x²–4y2

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Q: 2x -cos(2x)- 2x - (b) lim | x2

A:

Q: (fif2..f)is di fferentiable at x, proofthat ... by using f(x)– f(*.) f (x)=lim, x-x,

A:

Q: 4.x 2x 7e lim 1- e4x

A: We have to find limx→∞ e4x-7e2x1-e4x.

Q: Evaluate in terms of the constant a. lim (2a + x) x→ 0

A: To Determine:  Evaluate in terms of the constant a.…

Q: f (x+h)- f(x) 7x3-2x-1 Using lim-0 Find the slope of the tangent line y 5x+2 h at x = -1.

A:

Q: Find Lim-0.0 (r² + y²) In(x² +y²) '(xy)(0,0)

A:

Q: : limx->0(1/x3)

A: We have to simplify the given expression. The given expression is limx→01x3∫0xt2t4+1dt

Q: 4 Find lim х — 4 Væ – 2 x→4

A:

Q: (t³ + 8)-dt + 8)-šdt lim

A:

Q: Vx- 2 4. lim- x-2 x2 - 4 y-1 5. lim- Vy? +3 – 2

A: We can apply the limit to the expression by applying the limit as value for the variable in the…

Q: - m- J. lim x - 3 * x + 2 lim 2: *2x + 2'x² - x -6 3 m4 as x approaches m lim 2x – 12 lim x-+6 Vx –…

A: According to our guidelines, we can answer only 3 subparts of a question. Others can be reposted.

Q: Vx+4 -2 1 limx¬0 ||

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

Q: (a) lim x→2 arctan(7-3x)-" 2х-4 4 (b) 10-e5x lim x→00 16-x2

A: See the calculation and explanation below

Q: 12. Given f(x)=x² – 4x – 5. Find lim fx) –{2) x-2 2

A:

Q: ® Find Lim X->2 x¥ _ 2x² - 8 x² - 4 (2 ,X +2 Lim 3X X→3 X- 3 -3 X+3 O Lim © Lim t- fo -) ,X EO X+2 2

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

Q: Vx+1- /2x x² - x 2х f ) lim x→1

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: lim (x,y)-(-3,4) (x³ +3x²y² - 5y³ +1)

A: Here we have given an expression with limit and we have to solve it. We have lim (x,y)→(-3,4) (x3 +…

Q: lim y approaches 0  ................... [5y3 + 8y2]/[3y4 - 16y2]

A: Consider the given function as limy→05y3+8y23y4-16y2

Q: Along the path x = e find lim (2,y)→(1,0) y²+6zy 3x-y-3

A: To evaluate the given limit: lim(x,y)→(1,0)y2+6xy3x-y-3 along the path x=ey. Here,…

Q: y of -4 -2 -2 (a) (1) (b) lim f(x) x-1 2.

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: Q5/ Find the limits : 1- limp-0 3 V3h+1+1 x-1 2- lim-1 Jx+3-2

A: We have to evaluate the limits of:limh→033h+1+1limx→1x-1x+3-2

Q: of

A:

Q: If 2x – 2 0, find limf (x). x→1

A: We can use the sandwich theorem to solve this question.

Q: Q3) Find: (1) lim, V1+cos 2x (2) lim-2 (x+ 2) 14-x2

A:

Q: Find the limit.

A: We have to find the given limit

Q: Find limx∞ h(x), if it exists, f(x) = 5x3 − 3…

A: Given: fx=5x3-3

Q: 2x cos. X 17) lim --

A:

Q: V2x(x-1) 3. lim-1 Jx-1|

A: Given limit, limx→12xx-1x-1

Q: x+1 If f(x) = Solve to find lim f(x)? %3D Vx2+5-x'

A: Here is complete computation for your limit

Q: x² - 5x – 24 lim Calculate the limit: x-3 x+3

A: the given limit is: limx→-3x2-5x-24x+3 we have to evaluate the given limit.

Q: lim, S(x), given 7-4x. x < 1 S(x) = { %3D x² + 2 x 21

A: Given: fx=7-4x,  x&lt;1x2+2,  x≥1

Q: f(x+Ax)-f(x), Ff(x) = v2x + 1, what is the lim Дх--0 Ax

A:

Q: If V5 - 2r s f(x) < V5 - x for -1 sxs 1, find lim, 0 f(x).

A: Given: 5-2x2≤f(x)≤5-x2

Q: V4 - x2 0sx<2 lim f(x), where f(x) = < 2 9) x-4" 2 sx<4 x = 4 B) Does not exist A) 4 C) 2 D) 0

A: f(x)=4-x20≤x&lt;222≤x&lt;44x=4

Q: alignment at x² + x – 1 limx→ 2x2 — х + 1 has a horizontal at???

A: Topic = Limits

Q: x²+x5-2y lim (xy)-(3,9) %3D x-

A: Given limit lim(x,y)→(3,9)x2+xy-2yx-y

Q: -2x - 4 f) lim x--2 x + 2x ut | g) lim u-1 u3 1 4х — х2 h) lim x-4 2 - Vx Ya

A: As per our guideline we are supposed to answer only first three subparts. Kindly repost other parts.…

Q: Find lim (x2 + y?)ln(x² + y?) (x,y)-(0,0)

A: To findlim(x,y)→(0,0)(x2+y2)ln(x2+y2)