81. T a. Show that –x

Q: compute lim as x goes to pi/2 from the right of (x-pi/2)tan(x)

A: Given f(x)=x-π2 tanx To find limx→π2+f(x)=limx→π2+x-π2 tanx

Q: For the limit, sin(x² - y²) x² - y² if we approach along y-axis, we will get 0. Select one: O True O…

A: We know :- If we approach along y axis the x=0

Q: Evaluate the following limits using L'Hôpital's rule   2. lim x→0+ tanh x/sechx − 1

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Q: When using a graphing utility to generate a table to approximate. A student concluded that the limit…

A: Given,

Q: Find the following limits: (a) If lim x--> 3 ((?f(x)/2x) +1)?=2,find lim x→3 f(x) (b)  Find lim…

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Q: The following statement is incorrect: "If f has a horizontal asymptote y = L at ∞ , then the graph…

A: Solution: Consider the given function: f(x) = sin xx Determine limx→∞f(x) so, limx→∞f(x) = limx→∞sin…

Q: 1. Find the following limits. 2 sin(2x) – x (a) lim

A: Our Aim is to find the limit of the following expression given below:-limx→0 2 sin (2x)-xx-(i)

Q: D-the result of the following limit is 1² lim x-0 In (sec x)

A: Let's evaluate given limit.

Q: LEvaluate each of the following limits without using "L'Hôpital's Rule": 5-|x-4x2| 82x3+x2-8…

A: Indeterminate forms: The limit of A(x)B(x) when x→a when limit of both function exist and if both…

Q: lim, (5 イータ 1-Sint Cos C)

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Q: Evaluate the following limits. 2x sin- x 1. lim х-0 еx — х — 1 2. lim (sec x)cot × X-

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Q: Use continuity to evaluate the limit. lim 9 sin(x + sin(x))

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

A: We have to use L' Hopital' s Rule to evaluate the limit limx→∞1+4xx

Q: 3. Compute ahi-fin Lireh-fi for the following functions: and lim h40 a. f (x) = sin x

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Q: 1. Show using sequences of functions that lim -nz? e dx 0.

A: Solution is below

Q: Evaluate the following limit. Use l’Hôpital’s Rule when it is convenient and applicable.

A: Given: limx→0ex-sinx-1x4+8x3+12x2 given limit is in form of 00 we know that for 00 form we will use…

Q: 2. Use Squeeze Theorem to evaluate lim sin(sinh x) csch x 8118

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Q: Compute the following limits if they exist. sin x - (b) lim x→0 x tan x |

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

A: Given that: The limit is limx→0+ 3x+1x - 1sin x .

Q: Next qu Classify the statement as either true or false. If lim F(x) exists, then F could be…

A: We have to find out the continuous property

Q: Use L'Hospital's rule to determine the following limit: 1 tan x lim x+0+ x

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

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Q: Can we use L'Hospital's rule to find the following limit? 1- tan(x) lim ! cos((2 x) X-

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

A: If on substituting , one will get 00or ∞∞ form, one will use L-Hospital's rule, where one need to…

Q: Use L'Hôpital's Rule, if appropriate, to find each limit. ex-1 (a) lim x-0 tan x e2x -e-2x (b) lim…

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Q: Evaluate the following limit using L'Hospital's rule where appropriate. sin(11x) lim x→0 tan(6x)

A: We have to evaluate the following limit by using the L'Hospital rule.…

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

A: Use L’Hôpital’s rule to find the limits limx→0+lnx2+2xlnx.

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

A: Topic = limits

Q: Find the limit. sin(x – 3) lim х>3 x* + 5х — 24

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Q: 6 Compule the following limit lim glx) whene X-0 9 = (05 (2x) x९ o ( ৪-४, ४>0 where

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

A: We have to find the limit using L' Hospital's rule: limx→0sin x-xx3 We know in L' Hospital's rule we…

Q: What is the value of a if the limit of the function is 3, given by еах —1-ах lim X→0 ex2. = 3? -cos…

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Q: 30. Use the fact that lim x→0 sin x X = 1 (shown in video) to show lim x-0 1 - cos x X = 0

A: we will find the required.

Q: Using l'Hôpital's Rule, find the following limit: 5 - 5 cos x lim x-0 ex – x - 1

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Q: For the limit, lim (x,y)-(0,0) if we approach along x-axis, we will get 0. Select one: True sin(x² -…

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Q: O Determine the following limits O limx-0 3 1+y3x+1 sin 2x limx-0 10x"+x*+31 limx-too

A: We are allowed only 3 subparts of a question

Q: This question has several parts that must be completed sequentially. If you skip a part of the…

A:

Q: Evaluate lim w/ e 1- sin C x)

A: First , evaluate the limit. limx→∞ex3−1sin1x=limx→∞ex3−1limx→∞sin1x=e∞3−1sin1∞=e∞−1sin0=∞−10=∞0…

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: 1. Use a table of values to estimate the value of the limit. ex – 1 lim x-0 tan x

A: Given: fx=ex-1tanx limx→0ex-1tanx   Note: For tanx, x should be in radian.

Q: Evaluate the limit, using L'HÔpital's Rule if necessary. sin 3x 1. lim x→0 tan 8x In x5 2. lim x7 –…

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

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Q: If 2 - x2 <=g(x)<= 2 cos x for all x, find lim x-->0 g(x).

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Q: Refer to the graph of y = f(x) to the right to describe the behavior of lim f(x). Use - 0o and co…

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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: Find the following limits. Do not apply L'Hospital's rule. 2-4 lim x+2 |x – 2| (i) (ii) sin (3t) lim…

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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: lim x sin

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Q: Apply L'Hôpital's Rule a third time. 18 18x lim lim x-0 -sin x

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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.