Evaluate lim (sin z)an. 10.

Q: (b) Evaluate the followings (1) lim x? sin x-2 3х-2 (ii) lim X-00 2x+5

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Q: Evaluate using substitution.

A: We find the limit by substitution

Q: The value of lim in is nº (1+ n00 (1) e (2) e? (3) Ve (4) e 1

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Q: In which limits below can we use L'Hospital's Rule? 2x2 + 8x + 6 lim x2 + 6x - 9 2 00 e O lim e lim…

A: Please refer the attached image for complete solution.

Q: I. Evaluate the following limits. lim (sin x)tane x0+

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Q: a What shall be divided in both numerator and denominator to evaluate lim ? x0 sinß 00 b.Which is…

A: (a)Given , limx→0βsinβ We need to find the value with which the limit gets divided both in numerator…

Q: 5. Evaluate the following limits, explaining your reasoning: sin x – x (a) lim (b) lim (1+ x)/= I 00

A: Given the limit function

Q: an+1 an ? n00 ant+1 1. In the Ratio Test, is p equal to lim or lim n00 an

A: In ratio test:limn→∞ | an+1an|  or  limn→∞ |a nan+!|

Q: In evaluating 5 dx S²³² is same as evaluating lim (In(f(x))). Determine the value of f(x) if x=4.01.…

A: Given

Q: After direct substitution the limit lim (sinx)anx gives Select one: O 01 O 00 O 10 O None 00

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Q: Š Add your answer In evaluating dx is same as evaluating lim (In(f(x)){§). Determine the value of…

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Q: In evaluating x=3.98. dx x²-9 is same as evaluating lim (In(f(x))). Determine the value of f(x) if…

A: First we evaluate f(x) using substitution

Q: 22. Evaluate the following limits : x + Sinx 1+ Sinx a) lim b) lim 2x + 5

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: What is the value of 1 1+ lim T→5 1

A: We have to determine the value of the given limit

Q: xy Let f(x, y) and let L = lim2.y) ->(0,0) f(x, y). Which of the following 5æ2 + 3y2 statements is…

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Q: lim sin x 25 6 x -

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Q: +6 If q(x) = find lim q(x). Provide your answer below:

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Q: Use the graph and the viewing rectangle shown below the graph to find the indicated limit.

A: Graph of the function helps to find the limit of the given function. If the graph of the function…

Q: x + a Find the number a so that lim = 5. x + 3a Lütfen birini seçin: In 5 a. - 2 In 5 O b. 4. In 5 O…

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Q: 10sin (Tx) In (xº) q(x) What is lim g(x)?

A: solution :

Q: x? Find lim f(x), where f(x) = x + 5+ (x - 5)3 O A. 00 OB. Ос. 5 O D. -2 8.

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Q: 2.r The lim x² using L' Hospital's Rule, is: x>0 А. 1/2 В.О С.2 D. 00

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Q: ts sum. cos (an) If an=1000,evaluate lim %3D anta n=1

A: This question is related to topic series of real analysis. Solution is given below

Q: Given that lim (5x - 5) = 15, illustrate Definition 2 by finding values of d that correspond to ɛ =…

A: To Solve this problem we use here the definition of limit at a given point.

Q: Evaluate the following limits and and explain your reasoning. lim (0,n] (1 – -)e#dx n

A: Given: limn→∞ ∫0, n1-xn  ex2  dx We have to evaluate the given limits.

Q: Evaluate Limx→13 x²-1 O a. infinity 5 O b. 2 O C. 0 O d. none of these O e. 2²/33 25

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Q: If lim f(x) = 7, find lim f(x² %3D I→-1 O 49 O 7 O DNE O None of the choices

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Q: 2 ež h(x) 1 - 4 What is lim h(x)? x→+∞

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Q: 14. Find the error in the following incorrect calculation. Then calculate the limit correctly. lim…

A: Given limx→∞e-xx2

Q: In which limits below can we use L'Hospital's Rule? sin x O lim I/9 T/9 x x – 8 O lim 18 In(9- x) et…

A: The L-hospital's rule tells us that if we have an indeterminate form 0/0 or ∞/∞. All we need to do…

Q: neither lim f(x) nc

A: For the limit  fx and gx , take the condition . For function fx, fx=2 if x≥00 if x<0 The limit…

Q: lim –(x + 1) (exi – 1) еx+1

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Q: For the lim z (6x +) = 4, find the largest & that "works" for e = 0.0032. (Use decimal notation.…

A: Given,                    We have to find del.

Q: 8 lim is x0o 1+81/x А. 8 B. no limit C. D. 4 Е. О o| 8

A: Find limit of a function 8/1+81/x when x tends to infinity.

Q: is the below true and false and why? f'(x)=Limx->h (f(x+h)-f(x)

A: Given,  f'(x)=limx→hf(x+h)-f(x)

Q: If lim g(x) = 13 and lim h(x) = 23 then %3D [39(x) + 6h(x)] lim x6 2 O 26 O 88.5 O 46 O 36 O 19

A: The limit of a function at a point exists if both left-handed and right-handed limit exist and are…

Q: Theory and Examples

A: Consider a function fx and a point x=c. We know that the limit limx→cfx exists if both left limit…

Q: Find the value of lim f(x), if f(x) = 7x + 3 x 7 O 10 O 88 O 17 O 62

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Q: Evaluate the following limits. If you use l'Hospital's Rule, be sure to indicate when you are using…

A: We have given; (a) By applying the algebraic property, we get; Now we apply the L' Hospital rule…

Q: In x Find lim x o x2 Find lim x In x.

A: 2.

Q: 5 In evaluating 35₂ dx , is same as evaluating lim (In(f(x))). Determine the value of f(x) if…

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Q: 54. Let f(x) = [x] + [-x]. (a) For what values of a does lim,af(x) exist? (b) At what numbers is f…

A: (a) Given that: To calculate the value of “a” does the limits  exist,   For the given function,…

Q: Q2. Do as required 3. Evaluate: lim (-) X0 sinx

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Q: II. Evaluate the following limits. 1. lim sin x X→- 2

A: To find out the limit.

Q: Find the value of lim f(x), if x→6+ 6х + 5 5а + 6 x < 6 f (æ) = О 17 O 36 60 O11 O 66

A: Limit of the function

Q: 2 dx In evaluating is same as evaluating lim cosF(x))lc. Determine the value of f(x) if x=3.22 xV x2…

A: Solve the

Q: If 2 - x s g(x) s 2 cos x for all x, find lim,0 8(x).

A: Given,               2-x2≤g(x)≤2 cos(x), for all x And we have to find,      limx→0g(x)

Q: 56. Let f(x) = [x] + [-x]. (a) For what values of a does lim,-f(x) exist? (b) At what numbers is f…

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Q: L’Hôpital’s Rule is used incorrectly. Describe the error.

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Q: In evaluating S dx is same as evaluating lim C-3+ (In(f(x))). Determine the value of f(x) if x=3.4.

A: