(3) Sketch the graph and evaluate the lim→1 for the functions g and h, if possible. What can you conclude about the continuity of these functions? Explain. for r <1 (a) g(x) = Зх - 2 for x > 1 x² (b) h(x) = for a <1 %3D for x > 1 2х + 1

Q: Q.3 Find the following limits: x+3 3.1 lim→-3 x2+4x+3 x² +4x+3 x+2 3.2 limx-2 Jx² +5-3 u-1 3.3 lim-1…

A: As per the company guidelines we can solve first three parts . I hope that the given solution will…

Q: 1. Consider the function fx3x+2, -x-6, x>0x<0. Use table of values to find the limit of the…

A: The given function,  f(x)=x+2,x&gt;0-x-6,x&lt;0

Q: Note: You may need to assume the fact that  lim M→+∞ Mne−M = 0  for all n.Sales of the text Calculus…

A: To calculate the total future sale of the text.

Q: 4) Find the value of a for which the limit lim x→0 evaluate the limit. sin(ax)-sinx-x x3 is finite…

A: To Find: The value of a for which the limit limx→0sin(ax)-sin(x)-xx3 is finite and then evaluate the…

Q: Suppose f(– 1) = 0 g( - 1) = 0 f'(– 1) = 5 g'(– 1) = 4 and all functions are continuous. lim…

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Q: Find the constant a such that Va ax +4-2 lim

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Q: 2. Find the limits. limx→-1 sin(x² + 3x + 2) x³ + 1 M

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Q: Using the Nth term test for divergence, V5n-2 n2 n=1 diverges since lim V5n-2 n² is equal to n→∞ 8.

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Q: Let Sz+8 3x +8 I-1 Approximate lim f(z) numerically and verify your answer graphically. If it does…

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Q: tan 3h 3. Estimate the value of lim,0- by creating a table of function values for h h = 0.01,0.001,…

A: We need to substitute these values of h in function f(h) to evaluate limit

Q: 1 Discuss the existence of the limit lim sin x 0 x

A: To determine: The limit

Q: TX-1 t. Lim ×つ○ 1

A: limx→0 πx-12x2    +πx(e2πx-1)=limx→0 πe2πxx-πx-e2πx+1+2πx2x2 (e2πx-1)   limx→0 πx-12x2…

Q: 5) Find the indicated limit if it exists. Vx+4 – 2 a) lim x→0 8x' + 27 b) lim x→-1.5 2x+ 3

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Q: 8. e 1 Build a table to estimate lim x+0 X

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Q: Q1) A- Prove that: cotx = - tan-1x B- Find: 1. lịm 2. lim(v9x2 - x- 3x) cotx

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Q: 2. Use the paths x = y and x = 0 to verify the limit. lim (x.y)-(0,0) x2+y²,

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Q: (-1)"f" cost =1--+ 4! 2 (2n)! In(1+t) =t-+ 3 -.+(-1)*-"4 +... n Yukarıda verilen cost ve In(1+x)'in…

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Q: Because of their connection with secant lines, tangents, and instantaneous rates, limits of the form…

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Q: x- 2 x <4 Estimate lim Ax) where fx) = %3D x+2 x24 12 10 -8- 8. 6 2 Limit does not exist.

A: Check the value of function nearer to given point of limit if they are equal only then limit will…

Q: 4) Make a table for a sequence of carefully chosen values of a to estimate the limit 1® – 1 f(x) =…

A: By using table value of x for this given function to estimate this given limit

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: 2-メ Compite lim %3D Xラム z(T-X)

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Q: 5) a) If a > 0, compute lim a¯*. b) Which approaches its limit faster as x→», y=2* or y=x²?

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Q: lim is: X+ d X Does not exist

A: Use the definition of limit to solve this problem.

Q: The limit lim (n+1-vn- (A) equals-x (B) equals 1 (C) equals ( (D) equals +∞ O(E) does not exist

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Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) lim-(7/2)-(tan x)cosx (2) limy-0…

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Q: 5. Show that x³y³ lim (x,y) →(0,0) 2x¹2 + 3y4 does not exist.

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Q: Find the limit       lim h approaches 0   [(5h + 4)^1/2   - 2] /h

A: We have to find the limit of the given function: limh→05h+412-2h Since it is 00 indeterminate form…

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

A: Consider the equation

Q: Let ƒ(x) = (x2 - 1)/( | x| - 1). Make tables of the values of ƒ at values of x that approach c = -1…

A: Make tables of the values of ƒ at values of x .

Q: Find the limit: lim as x approaches 0 of (x^2-1)(2-cos x)

A: Use products of limit formula to find the limit as follows.

Q: Find the maximum value of & > 0 that satisfies the limit claim corresponding to e = 0.3, that is,…

A: In the question it is asked to calculate the maximum value of δ for the given function limx→59-x5=8

Q: -. Calculate each of the following limits, or explain why it does not converge. limx - 3 (x-2) /…

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Q: 9. Determine the exact answer for the following limit analytically: Vx+1-2 lim- x-3

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Q: Suppose that f(x) is a differentiable function (with a continuous derivative), such that f(0)=…

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Q: 3) If lim dt) = 5, can there be a vertical asymptote in the graph of d(f) at t = 0?

A: Given               :  limt→0- d(t)=5   Not Given       :  limt→0 d(t)=? limt→0+ d(t)=?

Q: Evaluate the limit x2 + 0x – 25 lim x - 5 x-5 Enter I for co, -I for -oo0, and DNE if the limit does…

A: we have to evaluate the following limit

Q: a. Graph h(x) = x2 cos (1/x3) to estimate limx--&gt;0 h(x), zooming in on the origin as necessary.…

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Q: Use numerical evidence to estimate the value of the limit to at least 2 decimal places. - x – 20 lim…

A: Here we have to evaluate the limit of given function

Q: Evaluate the limit V9n4 + 13n³ – 5n – 10 lim -V25n16 + 5n² – 9n Also, find the asymptotic value of…

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Q: Find the maximum value of 8 > 0 that satisfies the limit claim corresponding to ɛ = 0.1, that is,…

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Q: 9. Find the limit, if it exists. (If an answer does not exist, enter DNE.) Vx²+x a) lim X--00 -3x

A: topic- limits

Q: x-3x+5 by X-0 4x2+2x+3 10. Find the limit: lim means of the L'Hopital Rule

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Q: 4] [2M] Determine whether the limit exist in R for lim xsin(1/x²), (x# 0). x→0

A: Zero

Q: Consider g(x)=−7x3+7x2+9. a) limx→0−g(x)= b)limx→−1−g(x)= c)On what interval(s) is g(x)…

A: It can be solved using the limiting definition of continuity

Q: (b) Use the sandwich theorem to show that limy0x°cos - = 0. 1 In order to apply the sandwich…

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Q: Discuss the continuity of : Q1 x+ for *く0 for osr 2 Q2 1-x lim

A: