A portion of the graph of the function f (x) =v? is shown to the left. 4 We are examining the limit of f (x) at x = 2. The point (2, v7) is shown on the graph of the line. The limit of the function f (x) as x approaches 2 is /2. L=V2 Let e = 0.5. L-E What is the interval (L- , L+e)? -2 Write the interval (L – e, L + ɛ) as an inequality.

Q: Evaluate the limit using L 'Hospital's rule: lim x to 0 e^x -1/sin(12x)

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Q: Q1. By using the definition of the limit, discuss the limit of the function f:R - R if the value of…

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Q: Q3) Find the limit for the following function by using L'Hopital's Rule: x2. e* lim x→0 tan2 x

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Q: For the function given by q (x)= x² + 2x+1, use the limit definition of the derivative to compute…

A: Definition of the Derivative:        The derivative of f(x)  with respect to x is the function f'(x)…

Q: For the function f(x)= e^x cos(x^2), find the equation of the tangent line to the graph of f(x) at…

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Q: 4. Does f(x) = : (0, 00) → R have a right limit at x = 0? If yes, compute the limit. If not, explain…

A: We need to calculate when x->o+ from right side then f(x) exist or not.

Q: Q1. By using the definition of the limit, discuss the limit of the function f:R → R if the value of…

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Q: 1. If f(r) = x – 2, compute the following: a) f(1) = b) f(1+h} = c) f(1+h) – f(1) Bring your answer…

A: 2a) Given: The function is f(x)=x2-2   To determine: f'(1)=limh→0f(1+h)-f(1)h

Q: Evaluate the limit using a definite integral 2 lim n n 1+

A: Let x = i/n Hence, dx = 1/n when i = 1; x = 1/n; As n tends to infinity, 1/n tends to zero. Hence,…

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

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Q: sin x 1 y = X -1 1 X

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Q: The graph of a function is shown. AY (a) Does f(x) have a limit at x = a, as x approaches a? O Yes O…

A: a) When we use limit x=a means that the value of x is approch to value of a. Hence x approaches a…

Q: Express the limit as a definite integral. lim 40 E xk A xk; [-5, 1] k=1 1 9x8 dx -5 x9 dx x9 dx x dx

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Q: Explain the steps used to apply l’Hôpital’s Rule to a limit of theform 0/0.

A: From the given data:

Q: . Which statement is TRUE about the limit of the function f as x approaches 1? sx – 1 if x > 1 (-x²…

A: A. The limit of f as x approaches 1 is 0 False explanation :- The limit of f as x approaches 1 is…

Q: Question: What is the notation for "the limit as x approaches a from above of the function f (x) is…

A: Here we write the notation of the above statement.

Q: Use L' Hopital's to find the limit as x approaches positive infinity of:  (e^(3x))/(x^(2)) I hope…

A: We use the L'hopitals rule. For that differentiate the numerator and denominator with respect to x.…

Q: Compute the limit as x approaches infinity of x^e-x

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Q: What is the limit of (e^x-e^-x)/( sin (x)) as x approaches 0?

A: we have find the value of limx→0ex-e-xsin x

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

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Q: Calculate the limit for the function f(x) = Ex + 4 over the interval [0, 4]. Verify your answer by…

A: Given the function

Q: Can i get step by step help please

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Q: When using the definition of limit to prove that L is the limit of f(x) as x approaches c, you find…

A: The ε-δ definition of a limit is an algebraically precise formulation of evaluating the limit of a…

Q: Determine the value of the following limit and show that it exists. x² tan (x) lim (1,y)→(0,0) x2 +…

A: Limit exists and limit value is 0.

Q: 2. Given the function y = [(x-1)3 – 1]/(x), (x#0), find: (a) the limit of y as x approaches 0. (b)…

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Q: Why is the following function not differentiable at x = 1? 2- O the left handed limit of f(x) does…

A: Consider the graph of a function f(x)

Q: Find the limit of xsinx as x approaches 0

A: Given:

Q: Let 3z - 4x2 for z <0 3z2 + 3z forI20 | f(z) = { %3D ccording to the definition of the derivative,…

A: Topic  =Limits

Q: Q1. By using the definition of the limit, discuss the limit of the function f:RRif the value of the…

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Q: Evaluate the function f(x) at the given numbers (correct to six decimal places) (x)=3ex х2 3 Зx , x…

A: The given function:

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: 7. Find the limit as x approaches 0. F V I 2 2 O infinity O limit does not exist Oo .

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Q: 1 (a) What type of discontinuity does the function g(x)=- have at el/x – 1 x=0 ? Explain. (b) For…

A: This question is from limits and continuity.

Q: Q1. By using the definition of the limit, discuss the limit of the function f:R → R if the value of…

A: If the value of the function f:R→R is defined at x0∈R, such that To discuss the limit if the…

Q: The graph of a function is shown. a (a) Does f(x) have a limit at x = a, as x approaches a? Yes O No…

A: We have to define following questions regarding to the given graph

Q: Use two different methods to find the limit where m &gt; 0, n &gt; 0, and x &gt; 0

A: The given limit is: limx→∞lnxmlnxn where, m &gt; 0, n &gt; 0, and x &gt; 0 First method: To evaluate…

Q: Q.3: Discuss the limit of f (x) = - at x = 0¬, 0*,-∞, +∞, with graphs. %3D

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

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Q: find the limit f(x)= (5-x)/x2-25 a) find the x values at which discountous b) which…

A: NOTE: Refresh your page if you can't see any equations. . to find the undefined point, take…

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

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Q: Q1. By using the definition of the limit, discuss the limit of the function f: R → R if the value of…

A: For x not equal to 0, f(x) = xsin(1/x)

Q: Find: a. f (0) b. limit of f (x) as x approaches 2 from the left c. limit of f (x) as x…

A: We have to find

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

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Q: To apply the divergence test for Σ „5/4n² n=1 we need to evaluate lim eS/4n?. n→∞ What is the value…

A: Here we have to find the value of the limit.

Q: -5x? + 2x for æ 0 According to the definition of derivative, to compute f'(0), we need to compute…

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Q: Find the limit using l'Hospital's rule when appropriate. Find the limit as x approaches 0 of…

A: L'Hospital Rule :-  If a function f(x)=p(x)q(x)  then limx→af(x)=limx→ap(x)q(x) is of the form 00…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.