Suppose lim f (x) = 5, lim g (x) = 6, and f (x) 2 III. 5 < lim h (x)< 6

Q: 8. Find the indicated limit 2X √x + 1] X lim(- X→∞0

A:

Q: 2) Show that the_lim. 1) xy2 lim (x,y)→(0,0) x² +y²

A:

Q: Q.3 Find the following limits: x+3 3.1 lim→-3 x2+4x+3 x² +4x+3 x+2 3.2 limx-2 Jx² +5-3 u-1 3.3 lim-1…

A: As per the company guidelines we can solve first three parts . I hope that the given solution will…

Q: x – 4 8. Prove that lim Vx = 2 using the e-d-definition. Hint: Va – 2 = VT + 2

A: The epsilon-delta definition of limits says that the limit of f(x) at x=c is  value  of limit. if…

Q: 2. Compute the following limits at infinity and give reasons for your answers. 1 a) lim b) lim I00…

A:

Q: 1. Use the definition to show that x² - y² lim (x,y)→(0,0) x² - y² = 0.

A:

Q: 3x lim x→0 x2 + 2x

A:

Q: Verify the limits in a given equation below. (x+h)²-h² lim X→0

A: Verify itx→0lim(x+h)2-h2x

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: If x s f(x) s x² for x in [-1, 1] and x? x 1, at what points c do you automatically know lim, c…

A:

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 by interpreting the expression as an appropriate derivative. e2x 1 lim- = i x→0 X

A:

Q: Find lim x^2 − 3x + 2/x^3 − 2x^2 as (a) x → 0+ (b) x → 2+ (c) x → 2−

A: We are authorized to answer three subparts at a time, since you have not mentioned which part you…

Q: Evalate the limit 6. lim (e + x)²/x

A:

Q: 9. Given that limx→3 f(x) = 2 and limx→3 g(x) = −5 compute the following limits: (a) limx→3 2f(x)…

A: Given that limx→3f(x)=2 and limx→3g(x)=-5

Q: 2. Write the equation of a function that is discontinuous at x=5, but lim f(x) exists, and is…

A:

Q: Suppose that on the interval (2,5) f(x) less than or equal to g (x) less or equal to h (x) and Lim…

A: We have the following information.

Q: Q2 e valuat of the fallowing 2. ☺ lim L(x +3)t -16] xーース ☺ lim -25 X+5 メー5 lim |-X 3+X 9. X-3 メー] O…

A: To evaluate the given limits.

Q: Find the value of the limit: 3x -9x e -e lim In(1+x)

A: Using limit to find the value of given function

Q: 8. e 1 Build a table to estimate lim x+0 X

A:

Q: Evaluate lim as x approaches negative infinity 3e^2x + 4e^-x / e^2x - 2e^-x .

A: Limit of a function determines the continuity of a function. Three types of limits exist, one is…

Q: Given limx→3 f(x) = 5, limx→3 g(x) = −2, and limx→3 h(x)= −3, find the following limits a. limx→3…

A:

Q: Verify the limits in a given equation below. (2х-4)2 lim X→3 x+1

A:

Q: Use l'Hôpital's rule to find the limits x- 2 7. lim X2x - 4 x? - 25 8. lim -s x+ 5

A: l'Hospital rule is used when the value of the function is not defined by directly substituting the…

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

A: solution is given below..

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

A:

Q: 2) If x3 s f(x) sx for x in [-1,1), find lim f(x) if it exists. x-0 A) 0 B) Does not exist C) -1 D)…

A:

Q: Which of the following limits can be evaluated using L'Hôpital's Rule? Зх- 12 A.lim x→4 x2 +16 Зx-12…

A:

Q: 5x2 + 10x + 1 20. lim x* + x² + 1

A:

Q: 16. If f(x) = 2x – 1, what is lim x+h h B. - С. —2 D. 2 NIN

A:

Q: If 3x s f(x) sx +2 for 0sxs 2, evaluate lim f(x).

A:

Q: i. Calculate the following limit: 2x|x – 1| lim - x-1 x-1 ii. Determine the limit of f(x) when x…

A:

Q: Find the limit L. Vx - 3 1 lim X 4 X- 4 L =

A: After the substitution of limits the function gives an indeterminate form 00.

Q: 28. Assuming that lim f(x) = 4, compute: 1 (b) lim x+6 f(x) (a) lim f(x)² (c) lim x/f(x)

A: limx-&gt;6f(x)=4

Q: Find the value of the positive constant c such that....

A: Given- limx→∞x-cx+cx=14 To find- The value of c. Concept Used- If any limit of the function fxgx in…

Q: Find the limit. 4) lim (e5/x - 6x)\/2 x-0+

A:

Q: 1. If V5 - 2x² s f(x) s V5- x? for -1sxS1, find lim,-o f(x).

A: Answer and explanation is given below...

Q: Given n ≥ 0;  explain that   limx→∞ fn(x)/(e^x) = 0.

A:

Q: S -2x? + 5x 7x² – 5 for x 0. According to the alternate form of the definition of the derivative,…

A: Given:

Q: —ах+6 if x2-1 Let f(x)=< For what value of a does 2x2 +ах ifx<-1 lim f(x) exist? x--1

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: 4. Evaluate the following limits. 2* a. lim 3x² -3/x e b. lim x+0 x² 2 In5 x c. limx→→+00 x² 1000 In…

A: This question is related to topic limit of function.

Q: Find the limit. lim x → 2− e3/(2 − x)

A: To find the limit of the function

Q: Evaluate the following limits.

A:

Q: 2f(x) + 3x – х — 1 15 - Suppose that lim 5. Find lim f(x).|

A:

Q: Evaluate the following limits. 2. e* + e-*-2 a) lim b) lim (1 +2x) 3/ 3/x x2 c) lim x2 In x x-0*

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: 5x2 + 10х + 1 :0. lim x4 + x? + 1

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.