Find the limit ast approaches 7 for the function f(t) = 3(t- 9)(t- 8) lim 3(t-9)(t-8) = t-7 (Simplify your answer.)

Q: 2n3 +1 1 Prove, using definition of limit, that lim 4n3 – n 2 n-00 -

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Q: Let (7z 2x2 for I<0, 8z2 + 7x for r20. f(1) = According to the definition of the derivative, to…

A: Given : Derivative any function is as follows let   f(x)= xm

Q: Find the limit algebraically. ( f(-3 + h) – f(-3) lim h0 where f(x) = -3x2 + 2x + 9

A: Our objective is to find the limit algebraically.

Q: 1) Find the Limit lim/→0 3x²h-7th+h h

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Q: Use l'Hôpital's Rule to evaluate the limit. .3 8x +7 2, lim X- 1 X1 O A. 11 O B. 19 C. O C. - 16 D.…

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Q: Find the limit lim Vz +1 Enter I for o0, -I for-oo, and DNE if the limit does not exist. Answer

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Q: Let f(x) = /3r – 10. According to the definition, f'(r) = lim h0 (Enter the limit in reduced form)

A: f(x)=3x-10f'(x)=limh→0f(x+h)-f(x)h

Q: Find the limit. 3e - 3 V1 + t - 1 4 lim 1 +t/

A: We have to find the limit of this Vector. If the limit 0/0 form, then we can use L' Hospital rule.…

Q: Find the limit (if it exists).

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

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Q: Find the limits lim(2 - 3 as 1/3 a. t→0* b. t-0

A: Given function is: ft=2-3t13 As t→0+ we get, limt→0+ft=limt→0+2-3t13=2-∞=-∞

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: What is lim f(z) z→1 9(2) given f(x) = e2" and g(x) 3x2 – 3x + 6 ?

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

A: Given limit: limh→0 33h+1+1

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: What is the limit of f(x) = 8 as x approaches n? (If an answer does not exist, enter DNE.

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Q: Evaluate the limit 3(y²1) lim y 4 7y²(y-1)³

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Q: Find the limit. 5xz - 7xy P (1, - 1, 0) x2 + y2 - z2 lim %3D O 5 7/2

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Q: x² + x lim * + 2x + x³

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Q: Find the limit: o-4t 6. lim t→0 4 – 13' 17 + t to

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Q: What is the limit of f (x) = 1 as x → T?

A: Value of a constant function is always same irrespective of input.

Q: Find the limit limit x tends to (1/2) 4x(3x+4)2

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Q: Find the limit.

A: To find the limits

Q: Find the pointwise limit lim_(n→∞)(ex/n/n) for x ∈ R.

A: We find the pointwise limit  lim_(n→∞)(ex/n/n) for x ∈ R.

Q: find the limit as x approaches infinity of (1+2/x)^x

A: Find the limit as x to infinity,

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: Evaluate f(4+ h) – f(4) lim h0 where f(x) =5x +7. If the limit does not exist enter DNE. Limit =

A: f(x)=5x+7

Q: Q2: Find the limit x + 3 lim x→-3 x2 + 4x + 3

A: We have to find limit

Q: Find the limits in Exercise

A: Given : limh→055h+4+4

Q: lim -y3-3y²+4 y--2 -2y2-y+6

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Q: Find the limit V1+t4 dt lim

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Q: What is the limit of f(x) = 1 as x ➔ rr?

A: given fx=1

Q: What is the limit of f(x) = 4 as x approaches ?

A: Given fuction is fx=4. Here, given function is constant. So, for any value of x value of function…

Q: find the limit as x approaches to infinity (x-3 / x+1)^x/a

A: We need to evaluate the value of the following limit limx→∞x-3x+1xa Formula Used:  limx→∞1+mxx = em…

Q: Find f'(a) using the limit definition for f(x) = V10x + 7. f'(a) = %3D

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Q: nd the limit. e3x p-3x lim x→0e3X - e-3x

A: on solving this we get the

Q: Find the limit of x^x as x approaches 0 from the right.

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Q: Q8:- Find the limit of the following functions:- x2 - 2xy + y (1) Lim (х,у) —>(0,0) X+y ху — у — 2х…

A: First we simply numerator by applying appropriate identities or factorization of it

Q: Evaluate the limit V9n4 + 13n³ – 5n – 10 lim -V25n16 + 5n² – 9n Also, find the asymptotic value of…

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

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Q: T is discontinuous at -1 because lim f(x) as x--> -1 does not exist. * %23 .7. 5. %23

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Q: Find the limit as x approaches negative infinity of (xe1/x-x)

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Q: Find the limit: lim (1,y) → (0,0) x² + 8y?

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) (t + Δ)2-3(t + Δ) +…

A: The derivative of the function is calculated as follows.

Q: Find the limit x-1 lim x>I* Vx +2

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Q: Find the limit by numerically. 1 lim 1+ It| 1 |t – 1| t-0

A: Limit is the value of the expression as the independent variable approaches certain value, not…

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…

Q: Find the limit: (b) lim Sx+6 x-2

A: