Calculate the limit: lim(2x – 6x +1) Prove lim(3x – 2)=7. (Hint: Use the & – e definition of the limit.) 1.) 2.) fx² +4 if x+1 [2 3.) Find the limit: lim fS(x) if f(x) = if x=1 4.) Find the limit: lim x+1 5.) Find e so that f(x) is continuous on the entire number line. (x² j xs3 S(x) ={c if x>3 x² - 5x – 24 lim 6.) Calculate the limit: x+3 7.) Find the derivative of S(x) = 5x² + 2 using the limit definition of the derivative. 8.) Find the equation of the line tangent to the graph f(x) =" at the point (4,1). For problems 9 through 14, take the derivative. 9.) s(1) =x² - 10.) S(x) = 4 cos x + Vx 1.) у-х'sinx 12.) бх -5 y = x' +1

Q: Calculate the limit algebraically. (If an answer does not exist, enter DNE.) lim x→5   5 + X/X

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Q: b) Now, follow an algebraic approach to compute the limit 13 – 1 lim 1 I-1 and the limit V9+x– 3 lim

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Q: Find the limit if it exists, or show that it does not exist. lim (z,9)¬(0,0) zª + 4y²

A: Given:

Q: Find the limit, if it exists, or type N if it does not exist. lim(x,y)→(0,0)  2x^3+2y^3/x^2+y^2

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Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 1 lim 5 5 + x x--5

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Q: Use the two-path test to prove that the following limit does not exist. v4 - 2x2 lim (x.y)-(0,0) yª…

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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: Find the limit L.

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Q: Find the limit. (If the limit is infinite, enter 'o' or '-∞', as appropriate. If the limit does not…

A: limx->∞9-x3+x Divide the given expression by the highest denominator power So we divide each term…

Q: Evaluate the given limit. Show your complete solution. limx→∞ [e5z + x²]

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Q: find the limit or explain why it does not exist. lim In (t – 3)

A: limt->3+ln(t-3)

Q: Find the limit, if it exists. (If an answer does not exist, 3 - xy ху lim (x, y) → (2, 1) x² +2 +9y²

A: We will apply the limits.

Q: Determine whether the limit exists. If so, find its value. If the limit does not exist, indicate…

A: To evaluate the given limit substitute x=3 and y=2 in the given function.

Q: Consider lim e-. a) lim 4x - x² = 0 b) If we let t = 4x - , then we can rewrite the limit as lim of

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Q: 5h+4-2 Find the limit of : limħ=o

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Q: 7. Find the limit, if it exist x² +2 a. lim xV9 - x? C. im b. lim * x-1

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Q: Find the limit. lim væ+1

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Q: 1. Find the following limits mathematically. If the limit does not exist, state why. x* - 4x -12 a.…

A: When applying the limits to an expression and if we get a 00 form then use l'Hopitals rule to find…

Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim…

A: To evaluate the given limit: limx→83+x31-6x2+x3

Q: lim (1+e 9)º

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Q: Use the &-8 definition of e limit to prove lim+1 =2. x→5 5 nd the ɛ value when &=0.001.

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Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim…

A: The answer is given below:

Q: Find the limit L. Then use the e-8 definition to prove that the limit is L. lim x→-4 \2 L =

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Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.)…

A: Given limt→2 t2-32t2-3t+7now using the standard limit laws ,⇒…

Q: Find the limit L. Then use the - definition to prove that the limit Is L. lim (x² + 3) x-1 ||

A: We will find the limit.

Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) (2…

A: We have to calculate value of given limit.

Q: Find the limit: lim (x,4) → (5, –1) g4 + v2 %3D

A: We know that if a function f(x,y) is continuous at a point (a,b) , then lim(x,y)→(a,b)f(x,y)=f(a,b)…

Q: Use the definition of the limit (e – 8) to show that 1 lim - = i. 2+-i z

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Q: x" -1 :? x+1Vx -1 For a positive number nEN, what is the value of the limit lim-

A: On substituting x=1 in limx→1 xn-1x-1 tends to 00 (Indeterminate) form So upon applying L-Hospital…

Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim…

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Q: Find the limit, if it exists, or show that the limit does not exist. a) lim (x,y)→(0,0) 3x2+2y2/…

A: (a)-lim(x,y)→(0,0)(3x2+2y2x+1)Put the value (x,y)=(0,0)lim(x,y)→(0,0)(3x2+2y2x+1)=302+2020+1=0…

Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.)…

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Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 1 lim 7 x--7 7+ x 1

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Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim…

A: see below the answer

Q: xy-y lim - y(-1.2) (x + y + 1)

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Q: Find the limit. (If the limit is infinite, enter 'a' or '-s', as appropriate. If the limit does not…

A: Solve for the limit

Q: 2. Find the limit, if it exists, or show thaat the limit does not exists given ry - y lim…

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Q: Find the limit, if it exists, or show that the limit does not exist. 2 x² - 3y² lim (x,y)→(0,0) x² +…

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Q: Find the limit if it exists, or show that it does not exist. lim (7,v)>(0,0) xª + 4y²

A: According to the given information, it is required to find the limit of the given function.

Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) 2x2…

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Q: Find the limit. lim Vx X-1

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Q: Find the limit L. Then use the e-8 definition to prove that the limit is L. lim (x + 8)

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Q: Find the one-sided limit (if it exists). (If the limit does not exist, enter DNE.) -3 lim x-4-(x-4)²

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Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim…

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Q: Find the limit L. Then use the - definition to prove that the limit is L

A: To find the limit of the function x2+1 at x = 1   Left hand limit  limx→1- x2 + 1 = (1)2+1 = 2=…

Q: 3. Find the limit, if it exists, or show that the limits does not exist. d) lim (1,y)¬(0,0) xª + y²°

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Q: 4. Find the limit or show that it does not exist 2xy a. lim (x.y)-(1,1) x²+2y² 2xy b. lim (xy)-(0,0)…

A: First we have to solve a. Given: lim(x,y)→(1,1) 2xyx2+2y2 First we evaluate: lim(x,y)→(1,1) 2xyx2…

Q: Given that lim,+ f(x) = 3,lim,++0 9(x) = -5,lim→+0 h(x) = 0. Find the following limit,if it does…

A: • If the limit is finite and unique, we say that the limit exists.

Q: Construct a table and find the indicated limit. Vx +2 If h(x) = then find lim h(x). х-2 X→2 Complete…

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Q: Find the limit L. Then use the ɛ-8 definition to prove that the limit lim V6x x→0 L =

A: Here we have to find the limit L=limx→06x3