Evaluate the limit in terms of the constants involved: lim (9t - 4at +4a) = −27+16a −27+16a((−3)) t→-3

Q: Vx- 3 - 3 6. Find lim x→12 X-12 %3D

A: Given limit is  Firstly, we will multiply both numerator and denominator by sqrt(x-3)+3

Q: -2X-4 O lim x³+2x? X-2

A:

Q: Let f(x) = 5x² to f(6 + h). ƒ(6 + h) − ƒ(6) = 6x + 6. If f(6) = 150 and h = 5, determine the amount…

A: Given function:- fx=5x2-6x+6

Q: Vx+3x² limx¬0 X→∞ 4х-1

A:

Q: Calculate limx→∞(√x2+1−√x2−1).

A: The limit of any function at any point x=a is the value which the function has tendency to acquire…

Q: 5x3+8х2 2. Find lim х30 Зx4—16х2

A:

Q: Find the quotient of (x/2 - 2/x) and (1 - x2/4). What are the restrictions on the variable?

A: We have to find the quotient of the given two expression.

Q: 1. For the function f(x) = 3x² - 5x +7 find: a. f(-2) %3D b. f(-a)

A: Please see the below picture for detailed solution.

Q: Give the domain for t(x)= x+1/x2-3x-18

A: Given function is,

Q: 8. Describe the domain for h(x) = √70-9x - x²

A: To describe the domain for .

Q: 5x' +8x² lim x→0 3x* – 16 r? 3

A: Cancel out the common factor from numerator and denominator than put the x and calculate limit.

Q: If f(x) = 3x² -x, then lim (x+ h) – f(x) ; h A B 6x - 1e C бх +3h — 1€ D Зх — 1€ E 6x+h– 1e

A: Derivative

Q: (d) lim LI-IX √x²+2x+1 x² - 1

A:

Q: 4х+2 1. lim 9x² -3 2

A:

Q: Find the discriminant of: f(x)=(5x+4)(2x+2)

A:

Q: Find domain, range, asymptote, yintercept, and xintercept for f(x)=In(x+3)+3

A: Given: f(x)=In(x+3)+3 To find domain, range, asymptote, y- intercept and x- intercept.

Q: 0.Lim ュー)×40,2 メ-2 メ→o “波 (1+x) - 1 4)Lim *キX メーフ。

A: In this question , we can find the limit .

Q: d) lim √x²+x-3 - 2x

A: given limit

Q: 3- 5V+811 lim -00 2/2+2-162 t3-5v

A: After initial observation, I can see there is difference of variable in the limit 'x' and variable…

Q: Given the functions defined by f(x) = 6x² – 2 and g(x) = x² + 3, calculate the following: (g •f)(5)…

A:

Q: Jx²+2 Lim X-7 3x -6

A:

Q: What is the upper and lower limit for the function : f(x) = −12x2 − 37x − 21

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: Find the domain of: f(x) = 7x - 2/ x+4

A: Please refer the attached image for complete solution.

Q: (d). Lim    x +6x3     x →0   4x + 7x²

A:

Q: e*+3x-4 mx→0 3x+1

A: