check whether the limit exist at x = 1. Justify your answer.  ii. test whether the limit is continuous at x

Q: . Does the existence and value of the limit of a function ƒ(x) as x approaches c ever depend on what…

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Q: use the formal definition of limit to prove that the function is continuous at c. g(x) = 1/(2x), c =…

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Q: xy - Y lim(x,y)→(1,0) (x − 1)² + y²

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Q: Let f(x) = Vx –- 2. f(8 + h) – f(8) Then lim h→0 h If the limit does not exist enter DNE

A: The limit of a function is the value of that function when its argument tends to a particular value.

Q: Is the limit of f (x) as x approaches c always equal to f (c)? Why or why not?

A: To prove :                   The limit of f(x) as x approaches c always equal to f(c). Answer :…

Q: Find the limit if it exists. V=f(x)

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Q: 2 Use the definition of continuity to show f (x) = is x+3 continuous at x=1. Whenever you find a…

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Q: Evaluate the limit, using L’Hôpital’s Rule if necessary.

A: The limit of a function limx→Xfx=Ymeans that value of  function f(x)f(x) can be as close to Y by…

Q: Show that the absolute-value function y = abs(x) = |x| is NOT differentiable at x = 0. (Hint: by…

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Q: By considering different paths of approach, show that the function below has no limit as…

A: Solve for given conditions

Q: Describe a case where f(x) has a limit but is not continuous?

A: We know, if the left-hand limit is equal to the right-hand limit, then the limit of the function…

Q: Evaluate the limit, if it exists. If a limit does not exist, type "DNE". V4 +h – 2 lim h→0 h

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Q: Estimate the limit numerically or state that the limit doesn't exist lim  h→0   5^h−1/h=

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

A: The value of this function is equal to 1 regardless of value of x as we can see below in graph.  So…

Q: Is it true or false: that a two sided limit of f(x) as x approches c exist if the value of f(c) does…

A: The statement is given as a two sided limit of f (x) as x approaches c exist if the value of f (c)…

Q: Calculate the limit or show it is nonexistent. ry²e lim (r,y)→(0,0) x² + 4y4

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Q: 2sin?y 4) lim y→180° 1-cosy

A: Apply the limits and evaluate

Q: Use L'Hôpital's Rule to evaluate the limit L.

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Q: Use the graph to determine the limit. (If an answer does not exist, enter DNE.) y (4, 2) C = 4 4 6 8…

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Q: Use L'Hospital's Rule to evaluate the given limit

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2e What is the limit of the function f (x) = as x + xo ? 1-e

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Q: Use the graph of y = f(x) and the given c-value to find the following, whenever they exist. (If the…

A: Let the left and the right limits of a function f(x) as x→c are given by, limx→c-f(x)=M    and…

Q: evaluate the limit using continuity. lim (x,y)→(1,1) x+y

A: limx,y→1,1ex2-e-y2x+y

Q: use the formal definition of limit to prove that thefunction is continuous at c. F(x) = √,9 - x, c =…

A: Given: Fx=9-x, c=5 we know that any functionfx is continuous at given point x=c if,…

Q: use the formal definition of limit to prove that thefunction is continuous at c.

A: We need to use the formal definition of limit to prove that thefunction is continuous at c.…

Q: Calculate the limit algebraically. lim (x + Jx)

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Q: Use l'Hospital's Rule to calculate the exact value of the limit ) as x→ 0- Az) fX) = e -1 and g(x) =…

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Q: Use L’Hospital’s Rule to find the following limit.lim x → ∞ x^e^−x^2

A: We assume y, then take ln on both sides.

Q: Evaluate the limits at the indicated values of x and y.

A: This question is related to limits, We will solve it using given information.

Q: Let f (x) = 2Vx + 1. Find f'(x), carefully evaluating the limit.

A: Given : f(x) = 2x+1 Using first principle of differentiation we get  f'(x)=limh→0 f(x+h)−f(x)h

Q: Evaluate the limit using L'Hospital's rule. limx→∞(x^5)(e^(−x^2))

A: Given limit is It is of indeterminate from (infinity/infinity),  Therefore, by applying L'Hospital…

Q: Question: How else might you define "the limit as x approaches a of the function f (x) is L"? 3.

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Q: use the formal definition of limit to prove that the function is continuous at c. h(x) = sqrt(2x -…

A: To show that the function is continuous at x=2 we will find the left and right-hand limit at x=2.

Q: If f(x) is continuous at x=a, then a slope exists at x=a.

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Q: ove that the limit as (x,y) →(0,0) of f(x,y)=(x²-y2)/(x²+y²) does not

A: Given f(x,y)=x2-y2x2+y2

Q: The limit: does not exist Select one: O True O False x² - y² lim (z,y) (0,0) 4x + 4y

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Q: Use the graph of f(x) in the figure to evaluate the function or analyze the limit. yA y = fx)/ 30 i…

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Q: What is the limit of f(x) = 5 as x approaches a? (If an answer does not exist, enter DNE.) dne Need…

A: Solve simply

Q: Use L’Hospital’s Rule to evaluate the given limit.

A: We have to evaluate the following limit using L Hospital's rule: limx→0x2+xsinx L Hospitals rule…

Q: Find Ilim(x,y) → (0,0); x² + y² whether the limit exists or not

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Q: „100

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Q: ) Determine whether the following limits exist either by giving a proof from first principles or…

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Q: Evaluate the following limits for h(x) 6x + 1, I 6 and Justify your answer. (0 lim h(r) (i) lin…

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Q: Use L'Hospital's Rule to find the limit as z approaches i of (1 + z^6) / (1 + z^18)

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Q: Let f(x) = Vx – 6. f(7 + h) – f(7) - Then lim h→0 h If the limit does not exist enter DNE.

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Q: By considering different paths of approach, show that the function below has no limit as…

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Q: Let 3t f(E)= t?4 Cost, Find the limit lim F(t)

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Q: V16 + h – 4 lim h>0 h

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Q: Does the existence and value of the limit of a function f(x) as x approaches a ever depend on what…

A: Yes, existence and value of the limit of a function f(x) as x approaches a depends on what happens…

Q: compute limit f(z)dz

A: As per the question we have to compute a conture integral of the complex function  f(z) = e-z / (z2…