Let f(x) = Vx - 1 if x>4 and f(x) = x² – 4x + 1 if x < 4. Find: %3D lim f(x) x→4

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: Find the limits limx→0+{1 + 1/x}x

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Q: find the limit of g(x) as x approaches the indicated value. 3x2 + 1 lim = X g(x)

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Q: b) Given f(x) = V5x + 1 , Find lim x+h)-s(x) ,when x > %3D h-0

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Q: Consider f(x)=x−9/x+4 a) As x→∞, f(x)→ b) As x→−∞, f(x)→ f(x)=10x+7/x−6 c)limx→∞f(x)=

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Q: Find the limit. lim 5x e* i %3D X→+o

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Q: Find the limit. cos(x) – 1 +x2 lim x-0 2x4

A: It is given that, limx→0cosx-1+12x22x4.

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

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Q: TX-1 t. Lim ×つ○ 1

A: limx→0 πx-12x2    +πx(e2πx-1)=limx→0 πe2πxx-πx-e2πx+1+2πx2x2 (e2πx-1)   limx→0 πx-12x2…

Q: x³ - 8x* +1x lim xa -5-14

A: Dear student our policy is to answer first one only in case of multiple question kindly repost the…

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

A: limx→13x2+1gx=∞

Q: Find the limits limx→q(ln x)1/x

A: Given,     limx→qln x1x

Q: Let lim,-0+ f(x) = -2, where 8r - 3 for r <0 f(x): | 4x – 2 for r2 0 f(r) = Then what is (the…

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Q: 2. Use the paths x = y and x = 0 to verify the limit. lim (x.y)-(0,0) x2+y²,

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Q: Compute the limit 1 a2 1 - x2 lim xa x а - What can you say about the derivative of f(x) = ?

A: Given limit :

Q: Evaluate in terms of the constant a. lim (2a + x) x→ 0

A: To Determine:  Evaluate in terms of the constant a.…

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: Evalute the lim sin5x/x(x-1) as x approaches 0.

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Q: Find the limit. (If an answer does not exist, enter DNE. Vx + 6 – 4 lim x→10 X – 10

A: Given that  limx→10x+6-4x-10 find out the limit for the given

Q: Find the limit as x approaches - 2 for the function f(x) = 12x + 1. %3D lim (12x+1) = X→-2

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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: If 2x 0, use the Squeeze Theorem to find lim g(x).

A: Given that : as per squeeze theorem

Q: Use a table of values to estimate tne value of the limit of lim Vx + 4 – 2 f(x) f(x) 2.

A: Consider: limx→0x+4-2x   Let fx=x+4-2x Since we have to calculate limit at 0 of fx=x+4-2x.  Make the…

Q: Evaluate the function f(x) = x / (√x + 1 − 1) at several x-values near 0 and use the results to…

A: To evaluate: limx→0xx+1-1 using value of function at several values of x near to 0. Solution: We…

Q: Find the limits limx→0+x-1/ln x

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Q: Find the limit. x²y lim (x,y) → (0,0) x² + 8y²

A: limx, y→0, 0x2yx2+8y2

Q: 1 Use a plot of f (x) = 4 Vx - 2 to estimate lim f(x) 4 メ→4 | numerically.

A: Given: f(x)=1x−2−4x−4Estimate:limx→4f(x)=?Graphically  and  Numericallly

Q: V9x² + 1 lim x +1

A: Given : limx→∞9x2+1x+1

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: Find the limit of the function along the x-axis xy lim (x.y)-(0,0) x2 + y?

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Q: If [ f(x)\dx<∞ show that limf(x)dx=0 k→∞00 1

A: We have to prove that given expression.

Q: Find the limit: lim, 0+ x(ln x)²

A: The given expression is: limx→0+x(ln x)2 Which is in 0×∞ form. So, convert it into ∞∞ form.…

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

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Q: find the lim as x approaches infinity when f(x)= (1-x)/2x

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Q: Find the limit analytically: 2-4x lim 40 5+3x x? - 2.x -15 lim x 5 2. 3. Find dy/dx of:

A: A number M is said to be the limit of a function f(x) at x=a if for any arbitrarily chosen positive…

Q: Find the limits of the functions below a) limr-3 x* sin x b) lim,

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Q: Use l’Hospital's Rule to show that lim 1+ X. = e. コ

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Q: Let fa)=S(-5-x2 + 23x +19 f Xチー6 if X= -6 calculate the following limits. ENter DNE if the liniit…

A: l

Q: + 34, find f '(x) using the definition f '(x) = lim h→0

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Q: Find the limits limx→e+(ln x)1/(x-e)

A: Limit:      x→e+limln x(x-e)=h→0limln (e+h)(e+h-e)

Q: Let F(x) = | 3e“ dt. Find lim F(x) if it exists. If the limit does not exist, explain why. x→0

A: see below the answer

Q: a) By graphing the function f(x)=(cos2x-cosx)/x2 and zooming in toward the point where the…

A: Graph: f(x)=cos(2x)-cos xx2f(x)=cos2x-sin2x-cos xx2

Q: Find the limit. lim X→- 47 Vx+ 15 cos (x+ 4x)

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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: Evaluate the following limits.

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Q: If x Vx sf(x)s -x+ 1for all positive x-values, then what is lim f(x)?

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Q: lim(x,y)->(0,0)  (4x2y)/(x2+y2)1/2

A: Given: lim(x,y)→(0,0)4x2yx2+y2         (1) To compute: The limit.