17.Let f(x)be a function such that limx→∞f(x)=∞             limx→−∞f(x)=7   limx→3+f(x)=∞            limx→3−f(x)=−∞ Determine the horizontal asymptote.y=Determine the vertical asymptote.x=

Q: 2(x-1)* - y² Lex-1)* +2y (d) Show lim does not exist.

A: Limit exist

Q: Find the slope of the tangent line to the parabola y=4x-x^2 at the point (1,3) 1) using the…

A: Given

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: Let Sz+8 3x +8 I-1 Approximate lim f(z) numerically and verify your answer graphically. If it does…

A:

Q: 2. Compute the following limits at infinity and give reasons for your answers. 1 a) lim b) lim 10 4x…

A: 2(g) Given limit is : limx→∞6x2-7x+14x3-7 To find the value of the limit.

Q: Determine the limit by sketching an appropriate graph. 0 sx < 2 2 sx < 4 lim f(x), where f(x) = x-2-…

A: Given that f(x)=4-x2     0≤x&lt;22               2≤x&lt;44               x=4We have to find limx→2-…

Q: Find the limit       lim h approaches 0  3/[3h + 1 + 1]^1/2

A: Given limit: limh→0 33h+1+1

Q: 1 Discuss the existence of the limit lim sin x 0 x

A: To determine: The limit

Q: Prove rigorously that lim lxl = 0.x→ 0

A:

Q: 2. Use the paths x = y and x = 0 to verify the limit. lim (x.y)-(0,0) x2+y²,

A:

Q: Express the limit as a derivative.

A: To express: limit limx→-1x3+1x+1 as a derivative. Concept used: Definition of derivative:…

Q: 8. Evaluate the limit by using a change of variable. x* - 1 Vx – 2 а. lim 8 x - 8 d. lim Vx – 2 27…

A: According to the L' Hopital rule, if the limit of a rational function, f(x)=N(x)D(x) , is to be…

Q: Q4)A) Find the following limits (for two only). x+1 1. limx→-1 x2-x-2 1-Vx 2. limx→1 1-x 2х 3.…

A:

Q: Let Fexy=4 Find Lim FAt and Lim FEX) X->2* 2 Does l tM fe) exist? Why zis FM cON tin-noss at X=27…

A: Answer

Q: B) Find the limits by using L.Hopital rule : x²–16 2. lim x→4 (Vx+5)-3

A: The function is a rule that associates or fixes a number to the particular point x. If , then the…

Q: x- 2 x <4 Estimate lim Ax) where fx) = %3D x+2 x24 12 10 -8- 8. 6 2 Limit does not exist.

A: Check the value of function nearer to given point of limit if they are equal only then limit will…

Q: 6. Calculate limit: lim tg x X→0 2-V4+3x

A: Here we have to calculate Limit =limx→0 tgx2-4+3x

Q: B) Find the limits by using L.Hopital rule: 7x 1. lim x-0 sin 2x x2-16 2. lim x-4 (Vx+5)-3

A:

Q: Evaluate the function f(x) = x / (√x + 1 − 1) at several x-values near 0 and use the results to…

A: To evaluate: limx→0xx+1-1 using value of function at several values of x near to 0. Solution: We…

Q: 2-メ Compite lim %3D Xラム z(T-X)

A:

Q: lim is: X+ d X Does not exist

A: Use the definition of limit to solve this problem.

Q: 5. Show that x³y³ lim (x,y) →(0,0) 2x¹2 + 3y4 does not exist.

A:

Q: B. Calculate the limits of the following functions.. 1. limx¬-1(2X2 + X + 4) 2. limy--2(y3 + 5y – 1)…

A:

Q: compute lim as x goes to infinity of ln(x)^1/ln(x)

A: Consider the equation

Q: Find the limit. x²y lim (x,y) → (0,0) x² + 8y²

A: limx, y→0, 0x2yx2+8y2

Q: (b) Show that lim (x.y)(0,0) 2x6 + y2 does not exist by letting (x, y)→(0, 0) along the curve y =…

A:

Q: Find the limit: lim as x approaches 0 of (x^2-1)(2-cos x)

A: Use products of limit formula to find the limit as follows.

Q: Show that the limit of the function does not exist xy lim (xy)-(0,0) x2 + y?

A: We have to show that limit of the function does not exist.

Q: Find the Limit et – 1 lim t→0+ t3

A:

Q: c- Show that the following limit does not exist (x² - y²) lim (x,y)-(0,0) x2 + y² 2

A: Given ; lim(x, y) -(0,0)[(x2-y2)/(x2+y2)]2.

Q: B) Find the limits by using L.Hopital rule: 7x 1. lim- X0 sin 2x -16 2. lim X-4 (Vx+5)-3

A:

Q: Find the limits limx→0(ex + x)1/x

A: Consider the given limit as limx→0ex+xx

Q: Show that xy lim (x,y)→(0,0) x2 + y8 does not exist.

A: If two different path have two different limit then limit does not exist . Now find the limit along…

Q: Suppose that f(x) is a differentiable function (with a continuous derivative), such that f(0)=…

A:

Q: 3) If lim dt) = 5, can there be a vertical asymptote in the graph of d(f) at t = 0?

A: Given               :  limt→0- d(t)=5   Not Given       :  limt→0 d(t)=? limt→0+ d(t)=?

Q: Q3: Choose A or B (one only) fx2 +2x x-6x if xs-2 if x>-2 A) Check the continuity of the function…

A: Since we have to choose only one part of the given question, therefore we choose part (A). To check…

Q: Suppose that f(x) is a differentiable function (with a continuous derivative), such that f(0)=f'(0)…

A:

Q: Find the limits limx→0+x (ln x)2

A: Consider : limx→0+x(ln2x). Modify the limit function. limx→0+(ln2x)1x…

Q: Evaluate the limit x2 + 0x – 25 lim x - 5 x-5 Enter I for co, -I for -oo0, and DNE if the limit does…

A: we have to evaluate the following limit

Q: Find the limits limx→e+(ln x)1/(x-e)

A: Limit:      x→e+limln x(x-e)=h→0limln (e+h)(e+h-e)

Q: 1. Calculate the limit numerically. lim(x + 11) x→2

A:

Q: x-3x+5 by X-0 4x2+2x+3 10. Find the limit: lim means of the L'Hopital Rule

A:

Q: a) By graphing the function f(x)=(cos2x-cosx)/x2 and zooming in toward the point where the…

A: Graph: f(x)=cos(2x)-cos xx2f(x)=cos2x-sin2x-cos xx2

Q: Consider g(x)=−7x3+7x2+9. a) limx→0−g(x)= b)limx→−1−g(x)= c)On what interval(s) is g(x)…

A: It can be solved using the limiting definition of continuity

Q: 2. Evaluate the limits numerically. x-1 a) lim x-1 vx+3-2 x² +3x+2 b) lim x--1 x2-x-2 cos(x)-1 c)…

A:

Q: Evaluate f(3 + h) – f(3) lim h-0 where f(x) = 4x + 2. If the limit does not exist enter DNE. Limit =

A:

Q: Find the limit of the function along the path y = 2x X-1 lim (x.y)-(0,0) y -1

A: We have to find the limit of the function along the path

Q: II- Calculer les limites suivantes: CS Scanned with Camx³x3+4x-5 0071-x II- Calculate the following…

A:

Q: Find g'(x) for g(x)=-x^2+3x+2 by using the limit definition of a derivative.  lim x-->0…

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: