I. Apply the different techniques in evaluating the each item, you have to show your work at each step. 1. lim sec(3x + t)

Q: Verify that L’Hôpital’s Rule applies and evaluate the limit.

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Q: Graph g(x) = x sin (1/x) to estimate limx→0 g(x), zooming in on the origin as necessary. b. Confirm…

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Q: b* – 1 Show numerically that for b = 2 and b = 4, lim x→0 appears to equal In 2 and In 4,…

A: Given limit:

Q: 2 4. lim x-3+ \3-x 4 9-x2,

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Q: Find tant r lim t

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Q: Approximate the value of 2x + x lim e" – 1 by substituting in 3 different values of x that get…

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Q: Construct a table to find the indicated limit.

A: Limit x tends to 2 means the value of the variable approaches towards 0 from both sides that is from…

Q: - Show that lim sin a =D0.

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

Q: If lim, » 1512i (z2 + 30z) = x + iy, what is the value of a

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Q: 1 Ask for the answer to limx(1– e* ).

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Q: 1 1 lim xV1+x

A: limx→01x1+x-1x=limx→01-1+xx1+x

Q: Use l’Hôpital’s Rule to find the limits

A: Given: limx→π2-sec7xcos3x we know that  secθ=1cosθ so, limx→π2-cos3xcos7x  00 form it is 00 form, so…

Q: If lim f"(x) = +00, then the trapezoid estimation Tn - f(x) dx O TRUE OFALSE can never be within…

A: Given,

Q: Exaluate the following limi- 1. lim to + x' xー>-○ x(- 2x2 +5) x° 2. lim sin 3(2x+1) ×ー>-ム 2 2x +1

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Q: Evaluate the limit: sin(13x) lim I-0 tan(7x)

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Q: Q2/Find the limiting values: lim Tan (4%) 必→。 O lim 7 7- x2

A: Explanation of the solution is given below...

Q: lim (sec x)cot x X-

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Q: Find the lim using l'Hospitals Rule tan (7x). Sin ( 8x) lim X>0

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Q: It can be shown that lim be¯b = 0. Use this fact to compute S*xe* dx.

A: Given: ∫1∞xe-xdx

Q: Use L’H0 spital’s Rule where appropriate

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Q: sin x 34. lim 1 - x o0-r

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Q: Find the limits sin 2x lim x00

A: The graph of sin 2x is obtained by horizontally compressing the graph of sin x but the range of the…

Q: sec(x) – sec(a) lim x - a

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: Find the Oimits :- sin 3y Lim Sin Jz8 Lim My JzO ot

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the limits

A: We first try to find the limit by substitution

Q: What is the lim, 0+ sin(y) In(y)?

A: limy→ 0+sinylny=limy→ 0+lny1sinyBy L'Hopital's rule,=limy→ 0+1y-cotycscy=limy→…

Q: E. Use L'Hopitals's rule to find lim (2 – r)tan(r=/2).

A: Topic = limits

Q: lim X- Sin X X3

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Q: Hws] lim x = 5 E 5e •Prove

A: Given sequence xj=5j-1j+2j∈N we have to find limj→∞xj limj→∞5j-1j+2=limj→∞j5-1jj1+2j       (Taking j…

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: Make a table of function evaluations near the limit and use this to estimate the value of the limi…

A: Given: f(x)=limx→0xsin)(x)

Q: V1+3x-1 lim Answer: 1 %3D

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Q: Evaluate limt-->0(tan 4t)/(t sec t) Without using L'Hospital's rule.

A: To calculate the required limit without using the indeterminate form

Q: - Find the Lim;t: O Lim Sinx メー0 12ナメ3 E. 4) Lm sint2 sino lim 下-日

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Q: How do you solve the limit of this graph?

A: x->-1^- means x is slightly less than -1.

Q: Approximate the value of et – 1 lim x→0 2x2 + X by substituting in 3 different values of x that get…

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Q: f(2) is continuos if lim f(z) =f(z,)

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Q: verify that L’Hôpital’s Rule applies and evaluate the limit.

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Q: Calculate the following limits, or explain why they diverge. x2 – 9 lim 1--3 x+3 lim 2x + sin 3x

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

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Q: 1 lim x→0 x sin x x2 О 14 O 1/7 О 16 O 1/5

A: To find limx → 0 1x sin x - 1x2

Q: 1 lim \3 Vx + 9/

A: Rationalization of an expression is done to remove the radical expression from the term. For…

Q: Find the following limits. Do not apply L'Hospital's rule. 2-4 lim +2 x– 2| (1) (ii) sin²(3r) lim…

A: According to question given:(i) limx→2x2-4x-2When x approaches 2 from right x-2=x-2When x approaches…

Q: Use l’Hôpital’s rule to find the limits

A: To find the limit, limt→0sin5t2t using l' Hopital's rule. Solution: The given limit is ,…

Q: Find each of the following limits. Since you use L'Hopitals Rule, explain why you use it lim 2?e…

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Q: Evaluate using Theorem 2 as necessary.

A: Given: limx→0 x2sin2(x)

Q: Evaluate: lim,2 (x – 2) (cot rx). - O 1

A: We have to find the limit of a given function as x approaches 2. Rewrite given function as

Q: Use the table of values and graph to evaluate the following limits a. limx→0 (1-cos5x/6x) b.…

A: limx→01-cos5x6x The graph of y=1-cos5x6x is, From the graph we can see that the value of 1-cos5x6x…

Q: 4. Find lim (sin¬ V)cschr. r0+

A: The given limit,         limx→0+sin-1xcschx