In(3x) EXAMPLE 3 Calculate lim SOLUTION Since In(3x) → o and → o as x - o, l'Hospital's Rule applies: 1/x In(3x) lim = lim x- * 3" Notice that the limit on the right side is now indeterminate of type . But instead of applying I'Hospital's Rule a second time as we did in this example we simplify the expression and see that a second application is unnecessary In(3x) lim 1/x = lim 1y-2/3 3 = lim X- 00 X- 00 X- 00

Q: 1 Find lim +3 using limit rules. 2.

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Q: There is a jump discontinuity at x = 1 and lim f(x) = 1

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Q: 18 To determine whether L'Hôpital's Rule applies to lim follow the same procedure as in step 1. X0…

A: To write that L-Hospital rule applies or not

Q: 4. Show that In x lim x→1 x – 1 1. (Hint: Note that In In x-ln 1 x-1 and interpret the limit as a…

A: Given: To prove that limx→1 ln xx-1=1 using the limit as a derivativeFormula:…

Q: 5. Find the limit or show that it does not exist. sin(x – 1) lim 2 x→1 x´ + x -2

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Q: Compute limit as x goes to infinity of (square root(2x^2+3x-1))/(7x+1)

A: =limx→∞2x2+3x-17x+1multiply and divide by x2=limx→∞2+3x-1x27x+1x2=2+3∞-1∞7∞+1∞=∞

Q: Estimate the limit numerically for lim- x-4 x2-3x-4 3.9 3.99 3.999 4 4.001 4.01 4.1 x – 4 x2 – 3x –…

A: Given :   limx-->  ( x-4)/( x2-3x-4)

Q: . lim (3 – 2e

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Q: Evaluate the limit |x – 4| lim x-4 x- 4 If the limit does not exist enter DNE. Limit =

A: →For existance of limit at any point,         Left hand limit(LHL) and right hand limit(RHL) at that…

Q: { if x -1 Calculate the following limits. If the limit doesn't exist but it makes sense cases where…

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Q: Suppose g(x)=4x^2-lnx is the derivative of f(x). Compute Lim x->0 (f(x+1)-f(1)/x) Please show steps…

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Q: What is the limit of (ln 2x+5)+4 as x approaches -1?

A: In the question it is asked to calculate the limit of following function given.

Q: Ali is trying to find the limit of a function which is expressed as L = lim x→0+ (1 + x)1/x . From…

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Q: 4 Find the limit: lim sin(x) (Enter undefined if the limit does not exist.)

A: The given limit limx→04x-4sin(x)

Q: What is the limit as x goes to infinity of (ln(x3 + 9) - ln(2x3 + 17x))?

A: Use quotient rule of logarithm to reduce the function as shown,

Q: What must be multiplied to both numerator and denomination of lim→2 3-г-1 SO 2-x that the limit will…

A: We have to find multiplication factor for given Limit.

Q: compute limit as x goes to 0 of (sin(x)-x)/(x^3)

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Q: compute lim as x goes to infinity of ln(x)^1/ln(x)

A: Consider the equation

Q: 2. Use L'Hospitaľ's Rule to find lim (1+ x)*

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Q: Estimate the limit numerically to two decimal places or state that the limit does not exist.

A: limx→23x−95x−25 Since we have an indeterminate form of type 00 Apply the L' Hospital's rule:…

Q: Show that 6x 3 if x 5 x + 9 has a jump discontinuity at 5 by calculating the limit as x approaches…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: If lim f(x) and lim f(x) exist but are not equal, then x = c is a(n) jump discontinuity. X-C- XC+ If…

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Q: For solving a limit problem lim f (x)(*) which is in the form of indeterminate power, here are the…

A: We have given limx→af(x)g(x) which is in the form of indeterminate powerlet y=limx→af(x)g(x) taking…

Q: Estimate the limit numerically  limx→4 √x−4/x−16=

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Q: Compute this limit to infinity   limx→∞ of (7x^3 + 2020x+ 4)/(πx^3+ 18x^2+ 12)

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Q: Lim of √x, as x approaches to 4. Prove using epsilon delta deffinition

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Q: According to the alternate form of the definition of the derivative, to compute f′(0), we need to…

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Q: Evaluate the limit 6| lim x→6 x - 6. If the limit does not exist enter DNE. Limit =

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Q: e4x – 1- 4x lim x2

A: topic - limit using l 'hospital rule

Q: what is the limit of  lim      xsinx / 2-2cosxx--0 problems online show l'hopitals rule but i was…

A: To determine the value of limit without using L hospital rule

Q: If a one sided limit can't be calculated by plugging in what are the steps you take to solve?…

A: To find the right-hand limit at x tends to 0 of the function

Q: 2. Use L'Hopitals's rule to find lim (-).

A: Given that: limx→0+1x-1ex-1

Q: Find the limit or show that it doesn't exist. 1-х-х2 a) limx→-o 2х2-7 V1+4x6 b) limx 2-х3

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Q: How do you evaluate the limit:  limx-->0 (1-cos(7t))/(sin(7t))   WITHOUT using L'Hospital's rule?

A: Since the given function is function of  variable t but in question limit is given for variable x.…

Q: lim(4x – 3) = 5 x→2

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Q: х2-2х-3 d) lim lim-3 х2-5х+6

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Q: In(x/4) z+4 x2 – 16 (Enter undefined if the limit does not exist.) Find the limit: lim

A: Solving the problem by finding the limit of the given expression.

Q: Suppose that lim as x approaches infinity of f(x) + x^2 = L for some number L. Then lim as x…

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Q: x2 + 2x + 1 lim x--2 x2 + x +1

A: There is no need for L hospital as the limit can be evaluated directly.

Q: EXAMPLE 5 A Limit That Does Not Exist numerically. Investigate lim sin graphically and

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Q: 2) If 2 – x2 < f (x) < 2+ 3x² whenever -1 < x < 1, use limit theorems to find lim0 f (x). Give all…

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Q: In(3x) EXAMPLE 3 Calculate lim x → 00 SOLUTION Since In (3x)→ ∞o and In (3x) 1/x lim x → 00 = lim…

A: Topic = Limits

Q: Find the limit, if it exists. 7x + 70 lim x-10 |x + 10|| Step 1 Recall that x+ 10 x2 -10 x < -10. |x…

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Q: Alice and Bob are trying to compute lim x→∞ of cos(x)/x   Both of them know that they only have to…

A: We know that the range of cosx is [-1, 1]. Therefore Therefore Alice is correct. Now,

Q: 3-Vx2+9 Without using L'Hopital's rule, find: lim-

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Q: Find the limits limx→∞(1 + 2x)1/(2 ln x)

A: Given, limx→∞1 + 2x12lnx We know that, limx→ac·fx=c·limx→afx⇒12limx→∞1+2x1lnx Now,…

Q: -x e lim In(1+4e-x)

A: The answer is 1/4