If /6 – 5x2 sf(x)sV6-x² for - 1sxs1, find lim f(x). N6-5x² lim f(x) = X→0 (Type an exact answer, using radicals as needed.)

Q: Find the following limits: 3x2 + 8 (a) lim -4x² + 5 x6 – 3x4 – 2 - (b) lim x4 – 3x + 1 -x2 + 2x – 7…

A: The limits can be solved by directly inserting the limits in the function. If the function shows an…

Q: Show that lim (x,y) →(0,0) 16x4 +9y¹2 4x² + 3y6 does not exist.

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

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Q: Suppose that lim 4f(x)+ 2x – 14 5. Find lim f(x). z→1 %3D z→1 x – 1

A: Given

Q: 2 4. lim x-3+ \3-x 4 9-x2,

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Q: Estimate the limit numerically if it exists. (If an answer does not exist, enter DNE.) lim x→+∞  7x2…

A: The given expression of the limit is: limx→+∞7x2+10x-12x2-2x

Q: Consider limx-4 f(x), where f(x) 14x+ 9. Find a maximum value of 6 such that: If(x) 65< 0.006 if |x…

A: Plug f(x)=14x+9 in the given inequality and simplify.

Q: Find limx-&gt;∞,if for all x&gt;5

A: We apply limx-&gt;∞ on all sides.

Q: For all x ≥ 0, 4x − 9 ≤ f(x) ≤ x 2 − 4x + 7. Find limx→4 f(x). ⇒

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Q: Vx2 – 9 4. lim х-з х — 3 X→3

A: Given limx→3x2-9x-3

Q: Find a Limit using factoring:

A: We have to find the limit using factoring: limx→1x2+2x-3x-1 This is 00 indeterminate form of limit.…

Q: Calculate the limit lim 2 / 5x-15 as x goes to 3^+

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Q: Use definiction to १r० v of Conkegene to lim n+4

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Q: If 2x - 2s f(x) sx² - 2x + 2 for x 2 0, find lim f(x). x-2

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

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Q: Show that lim (x,y)→(0,0) 16x4+9y12 4x²+3y6 does not exist.

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Q: Q4: Find the following limits if exist:-- x-1 x2-x 1) limx-1²+2x-3 2) limx-1 x²+3-2

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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: Find the indicated limit. 2x lim (- Vx2+1 X00

A: Find the indicated limitlimx→∞(2xx2+1)

Q: If √5 − 2x^2 ≤ g(x) ≤ √5 − x^2 for −1 ≤ x ≤ 1, find limx→0 g(x)

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Q: If 7-6x2 sf(x)s 7-x² for -1sxs 1, find lim f(x). X→0 lim f(x) =

A: If 7-6x2≤f(x)≤7-x2 for -1≤x≤1, we have to find limx→0f(x)

Q: Find lim (√2-t, et-¹, In(t + 1)) t-0

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Q: Let Fexy=4 Find Lim FAt and Lim FEX) X->2* 2 Does l tM fe) exist? Why zis FM cON tin-noss at X=27…

A: Answer

Q: Q3: (a) find the following limits if exist:- (1) limx-o √x+9-3 1-cosx xsinx (2) limx-07 (3) limx-1…

A: Topic = Limits

Q: 3. Use L'H rule to find lim (1– 2x)/=

A: From the given problem: limx→01-2x1x Let, y=limx→01-2x1x Now taking log on both sides.…

Q: Estimate the limit numerically if it exists. (If an answer does not exist, enter DNE.) lim x→+∞  5x2…

A: Consider the given function:

Q: Estimate the limit numerically. 3x² +270x+5 lim 2x+15 + oo

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

A: solution is given below..

Q: Is there a value of a for which limx1 3x^2+ax+a+3/x^2+x-2 exists? Enter the value of a if such a…

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Q: if f(5) = 4, f'(5) = 7, then lim of (f(x²+1) -4)/(x²-4) = ?? when x goes to 2

A: Please see the answer below.

Q: If f(x)=x2−9x−3 , what is limx→3+x2−9x−3 , limx→3−x2−9x−3, and f(3) ?   Is f(x) continuous at 3?

A: Given,              f(x) = x2 − 9x − 3

Q: (4) Find the indicated limits, if they exist: Зх—12 (a) lim→4Jx-2 x²+3x-4 (b) lim→-4 +4x x²+4x 3 cos…

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Q: Find the limit 1-ex lim x+0 10x2 – 18x

A: Here we have to use the concept of limit.

Q: Find the indicated if it exists: lim x to +infinity;  2x2+3x+1 divided by x4 - x2

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Q: 2. Use L'Hospitaľ's Rule to find lim (1+ x)*

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Q: If 5-4x sf(x)s5-x for - 1<xs1, find lim f(x), lim f(x)%= f(x) =D

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Q: Show that 16x4+9y12 lim (x,y)→(0,0) 4x²+3y6 does not exist.

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Q: Fird the domain of f (x) = 2-Vx2-5 Solve lim x→-3 =? (Don't use L'hopital Rule) x+3

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Q: . Is it possible that f(2) = 5 but limx→2 f(x) = 7? If so, what kind of function can satisfy this?

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Q: Find the limit analytically: 2-4x lim- 40 5+3x 1.

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Q: Show that 2 x² - y² - 1 lim (x,y) →(1,0) 1 − x + (2y)² - does not exist.

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Q: If 2x – 2 0, find limf (x). x→1

A: We can use the sandwich theorem to solve this question.

Q: Evaluate the limit. 5 sin(x) – 5x lim x3

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Q: Evaluate the limit 5 + 2x lim 8 – 8x x → 0

A: We haven the function is: f(x) = (5 + 2x)/(8 - 8x)  Dividing the numerator and the denominator by x…

Q: Find lim at inf: (x^2 + 2x)/(x - 7) Don't use L'H

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Q: If 3-2x sf(x)s3-x for -1sxs1, find lim f(x). lim f(x) =|

A: Calculate left hand limit and right hand limit than find the limit using sandwich theorem.

Q: Suppose that lim as x approaches infinity of f(x) + x^2 = L for some number L. Then lim as x…

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Q: 2) If 2 – x2 < f (x) < 2+ 3x² whenever -1 < x < 1, use limit theorems to find lim0 f (x). Give all…

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

A: