Suppose that f and g are continuous functions such that f(4) = 6 and lim[f(x) + 5g(x)] = 12. Find x-4 a) g(4): 5) lim g(x): x→4

Q: Find Limit Using Squeeze Theorem 2. If 2x – 2 < f (x) < x² – 4x + 3 for x 2 0, find lim f (x). - x→1

A:

Q: Evaluate the limit: lim_ (x - ln x)* x→0+

A: Using L Hospitals rule , Value of given limit is evaluated.

Q: Find the limit, if it exists.

A: The limit of a function limx→Xfx=Y means that value of  function f(x) can be as close to Y by making…

Q: Let f(x)={−2x+2  x≠1               {2   x=1. What is f(1)? If f(1) does not exist, type: 99999 What…

A:

Q: Show that the limit does not exist. (x + y)² lim (7,y)→(0,0) x² + y²

A: We have to check

Q: Let f : [1, ∞) → R be a continuous function such that lim|f(x)| = 0. For n ≥ 1, let gn : [1, ∞) →…

A:

Q: x²– y? lim (x, y)→(0, 0) x² + y?

A:

Q: Show the limit does not exist. lim (1,y)→(0,0) x6 + y²

A:

Q: 2. Find the limits. limx→-1 sin(x² + 3x + 2) x³ + 1 M

A:

Q: Find the limit. cos(x) – 1 +x2 lim x-0 2x4

A: It is given that, limx→0cosx-1+12x22x4.

Q: Evaluate the limit: lim (x - ln x)* x→0+

A:

Q: Let f(x)={−2x+2   x≠1               {−5         x=1. What is f(1)? If f(1) does not exist, type:…

A: Given,

Q: Find lim (x,y,z)-(0,0,0) x²+y2+z4 xy+yz?+xz2 if it exists, or show that the limit does not exist.

A:

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: Let f(x) = 2x² + 2x + 3. According to the definition, f'(x) = lim h→0 (Enter the limit in reduced…

A: the soluton is following.

Q: evauluate the limit lim x→0 (sin2 (3x))/ x2

A:

Q: Find the limit. lim x+v-1 (x, y)- Vx+y-1

A: The given limit is of 0/0 form. In this type of limit problems, we try to remove 0 from the…

Q: Show that the limit x²ycos y lim (x.y)→(0,0) 2x4 +y² does not exist.

A:

Q: Find the limit, if it exists

A:

Q: Find the limit. (x²-7) (6- cos x) lim

A: Given,           limx→0x2-76-cosx

Q: Evaluate the limit: sinx lim x→0 e4x – 1

A:

Q: For a certain function f(x, y). lim-0 f(t, 0) = 0 and lim 0 f(t, 3t) = 0. Does this mean that the…

A: Given- For a certain function fx,y it is given that limt→0ft,0=0 and limt→0ft,3t=0  To Check- If the…

Q: Find the limit of the transcendental function. lim e-2x sin Ax X→0

A: NOTE: Refresh your page if you can't see any equations. .

Q: 4 – V* lim x 0 2 + Vx

A:

Q: Let f(x) = 3x² – 5x + 1 f(x+h)-f(x) (a) Find f'(x) using the limit definition of derivative. That…

A:

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

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

Q: (a) Evaluate the following limit: lim ) (1-e3x x²+3x, x-0 (b) Find the equation of the tangent to…

A:

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: Estimate the limit numerically if it exists. (If an answer does not exist, enter DNE.) lim x→0  x −…

A: We have to estimate the limit numerically if it exists.  a) limx→0(x-3) b) limx→0(x-1)

Q: 2. Find the limit of the following function sin(x - 4) lim- x-0 x- 2

A:

Q: Show the limit lim (x,y)→(0,0) x4 + y² does not exist.

A:

Q: If [ f(x)\dx<∞ show that limf(x)dx=0 k→∞00 1

A: We have to prove that given expression.

Q: 9 -x2 if x 1 .What value of c makes g(x) continuous at x = 1? Show all conclusions. 2 Vx-4 Using…

A: For a function to be continuos, the left hand limit should be equal to the right hand limit.…

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

A:

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

A:

Q: Find the limit, if it exists.

A: First of all, use the limits property and apply the limits on numerator and denominator.

Q: Consider the function 2+2+17-2ry+v² if (r, y) # (0,0) f(r,y) = if (1, y) = (0,0). (b) Find…

A:

Q: If 2 - x2 &lt;=g(x)&lt;= 2 cos x for all x, find lim x--&gt;0 g(x).

A:

Q: Let fn → f, where if 0 <x < L3 (3 – x) if 1 < x<1 { fn (x) п-3 if 0 < x < 1 - and f(x) if x = 0 Then…

A:

Q: Find the limit. lim (2 – x) tan(3«) %3D x>1

A:

Q: Let F(x) = | 3e“ dt. Find lim F(x) if it exists. If the limit does not exist, explain why. x→0

A: see below the answer

Q: Find the limits: x² – x - а. lim x→1 In x e* – 1 b. lim x→0 sin x .3 c. lim С.

A: Limits using L'Hospital Rule

Q: If x Vx sf(x)s -x+ 1for all positive x-values, then what is lim f(x)?

A:

Q: |x| does not exist. Show that the limit lim x 0 X

A: Given: limx→0xx

Q: Find the limit. cos(x) – 1 +x² .2 lim 2x4

A: NOTE: Refresh your page if you can't see any equations. . apply L'Hopital's rule

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: