Find the limit of the rational function a. as x→o and b. as x→→ -∞. x+ 11 f(x) = x° +7 x+ 11 а. lim (Simplify your answer.) !3! x→c∞ x³ +7 X+11 b. lim (Simplify your answer.) %3D x→- 0 x° + 7

Q: z2 -6x +36 Find lim I +6 O 36 O 108 The limit does not exist.

A: To find limx→-6x2-6x+36x+6

Q: In the function:  f(x)= (3x^2)ln(x) , x>0 What are the vertical asymptotes?

A: Given function is,

Q: - f (x) = e¬² at c= 0

A: Given f(x)=e-x at c=0

Q: For the function given by q (x)= x² + 2x+1, use the limit definition of the derivative to compute…

A: Definition of the Derivative:        The derivative of f(x)  with respect to x is the function f'(x)…

Q: x2 + 0x – 4 lim x-2 x - 2 Enter I for oo, -l for -co, and DNE if the limit does not exist.

A:

Q: Using the Nth term test for divergence, V5n-2 n2 n=1 diverges since lim V5n-2 n² is equal to n→∞ 8.

A:

Q: given y= f(x)= 2^2-9x+20/x-4 Why is it not possible to apply the quotient limit theroem to find the…

A: Given function is:And the limit of x approaches 4. Hence, the limit is written as: Quotient limit…

Q: Find the limit of the exercise below.

A: Factor the numerator using a^2-b^2=(a+b)(a-b) formula. With a=t and b=4

Q: evaluate the limit:  limit of the square root of 1+t - square root of 1-t / t as t approaches 0

A:

Q: For n > 0, use Taylor's theorem to find (1+x)!/n – 1 lim 3.

A: Explanation of the answer is as follows

Q: Find the limit. 7e - 7 V1 + t - 1 9. lim t t 1 + t

A:

Q: Find the following limits: Vx+3-1 i. x-2 x+2 lim 1 + x-1- \]x-1| ii. lim x2 +3x, Vx+-7 lim X→+co…

A:

Q: Find the limit of the rational function (a) as x o and (b) as x- -o. Write co or - o Where appropH…

A: Given, fx = 5x3+4x3-x2+x+5  We have to find  (a)   limx→∞ 5x3 +4x3-x2+x+5  (b) limx→-∞ 5x3…

Q: If f(x) = /4² + bx – Vcx² – dæ has a horizon- tal asymptote at y = 2 for all x b+c+d. - Vcx2 - dx…

A:

Q: If y = f(x) and y = g(x) both have a vertical asymptote at x = a € R, then y = f(x) + g(x) has a…

A:

Q: Find the horizontal asymptotes of the function by computing the limits at infinity.

A: Asymptote of a function is a line the graph of a function approaches. Horizontal asymptote is a line…

Q: f(x) = x(3x-(9x2+2)1/2). Compute the limit of f(x) as x tends to positive infinity.

A: Given data:   The expression for the given function is f(x)=x(3x-(9x2+2)1/2).   The expression for…

Q: Find the horizontal asymptote(s) of the following if there are any. x3+2 y6-y2+7 1. f(x) = 2. h(y) =…

A:

Q: find the limit of rational function (a) as x→0 and (b) as x→ -o. 2x + 7 x3 – x² + x + 7 f(x)

A: Given that, f(x)=2x3+7x3-x2+x+7 Factoring out x3 on both numerator and denominator we get,…

Q: Q3: A- Find the limit for the following functions: - tan2x 4х-3 Зx3-9х2 +х-3 1- lim x→0 sin4x 2- lim…

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: find the limit of g(x) as x approaches the indicated value.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: find the limit of rational function (a) as x→0 and (b) as x→ -o. 2x + 3 f(x) 5x + 7

A: To evaluate: a)limx→∞2x+35x+7,b)limx→-∞2x+35x+7 Solution: a)limx→∞2x+35x+7 limx→∞2x+35x+7 On…

Q: If f has a vertical asymptote at x = c then f(c) does not exist. True False

A: Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a…

Q: lim f(x) = 81 (a) VF(x) (b) [3f(x)] (c) [f{x)]²

A: Using rules of limits.

Q: Determine the limit at infinity x+x-6x first.) x+x2-6x lim (x-x2 -6x) (Hint Multiply by O A. 0 OB. 6…

A: To Determine: Compute the limit

Q: Show that for any e > 0 and S, 1X₁, lim P(|S₁-81 ≥ 2) = 0. y'a 3140

A: We will use Chebychev's inequality to find the required limit of probability.

Q: 2. Given the function y = [(x-1)3 – 1]/(x), (x#0), find: (a) the limit of y as x approaches 0. (b)…

A:

Q: Find the value of b-2a for which the limit ex – xex – cosbx - limx +0 exists 4 Select one: а. 3 b. 1…

A: L'Hospital's rule is a useful method to find the limits of indeterminate form. There are two…

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

A:

Q: O3: A- Find the limit for the follo tan2x 1- lim x→0 sin4x

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Q3) Find the limits of the following functions V2+12-4 3.lim t2+t-2 tan3x lim X-0 sin8x 1. lím 2.…

A:

Q: Can i get help with this problem step by step?

A: Here, we rationalize the denominator to get the required value of limit.

Q: H.W/ using convolution theorem to find L-1

A: We have to find the Laplace inverse by using convolution theorem

Q: Find the polynomial f(x) of degree 6, 1/x which satisfies lim{1+ f(x)] =e? x3 X-0 and has local…

A:

Q: Find lim I→1 x² – 1 Enter inf for oo, -inf for -00, and DNE if the limit does not exist. Answer:

A: In such kind of limit we substitute the value of the limit with sign and then evaluate the…

Q: -1 sx3 O A) -0 O B) -1 O C) 7 O D) Does not exist

A:

Q: Use Dirichlet's principle with n = 10 to find a rational approximation of T.

A:

Q: Consider the function f(x, y): 5xy 2x2 + y? (a) State the domain of f(x, y). (b) Find the limit 5xy…

A: f(x, y)=5xy2x2+y2A)Domain f(x, y)The function is defined everywhere.Domain: (x, y) ∈ (R×R)

Q: [VALUATE THE LIMIT OF THE GIVEN FUNCTIONS: 3) Lim Jx-2 メ→2x-4

A:

Q: Evaluate the limit *dx – x – 4aª lim 3 A) В) 1 C) D) 4 E)

A:

Q: Find the limit: -3t e to - 1 t10 – t9' 2+ t -5 lim( t t→0

A:

Q: Find the limit of f(x) = as x approaches co and as x approaches - oo. 4 -

A: Given,          fx=-4+2x4-6x

Q: For f(x) = 2x³ - 2, find ƒ '(x) using the definition f '(x) = lim f(x+h)-f(x) h h→0 f'(x) = Using…

A: Let's find.

Q: find the limit of f(x)= ((x+h)^3-x^3)/h as h approaches 0

A: SOLUTION-

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: 13. Given the function f (x) = 2xv1 – x2. Determine the - c. Y intercept d. Vertical Asymptote(s)…

A:

Q: Find the Horizontal Asymptote(s) of f(x) = 1+

A: We have to identify the relative extrema according to the given information and find the horizontal…

Q: Find the limit as x approaches infinity of the function V2 – x2 h(x) х3 — х + 1

A: Given:  h(x)=2-x2x3-x+1h(x)=x2 2x2-1x31x3-1x2+1  (Taking highest power of x in the…