4) Evaluate the following limits. You may Use L'hopital's rule, IF it is valid to do so: a) lim 1-0 T b) lim - ²

Q: L'Hopital's Rule applies to which of the following limits? Indicate all the apply. Select all that…

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Q: b) Solve the limits of the following expressions. i) lim *-1 x→3 x+3' ii) x²+6x+9 lim x→-3 x+3

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Q: Sketch the graph of the parametric equations x = sint, y = 2 cos(3t), π ≤ t ≤ 27. Clearly label the…

A: We are to sketch the graph of the parametric equationsx = sint, y = 2 cos(3t), π < t < 2π.…

Q: Find each of the given limits, if they exist. Justify your responses (in other words, don't just…

A: In the given question the limits of the question has to be determined if they exist.

Q: 2) Find the limit for the following equations: a) lim (+1) x--1x²-x-2 x²-9 x-43 |x-31 b) lim

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Q: We can write lim as 40 sin 4x

A: Topic = Limits

Q: Using the € - 6 definition of limit, prove that x lim x 27x13 = : 2.

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Q: Use l’Hospital’s rule where applicable to find each limit.

A: Given,          limx→0+4xlnex-1

Q: e* a) lim x-0o x2-5 3 In x b) lim x0 ex+5

A: a) limx→∞exx2-5∞∞ form=L'Hlimx→∞ex2x∞∞ form=limx→∞ex2L'H=∞

Q: 1. Find the following limits, if they exist. If the limit does not exist, write "does not exist" and…

A: Evaluate the given limit  Limit is exist

Q: If lim f(x) = L, then f(a) = L. A) True B) False

A: We can find the value as below

Q: Evaluate the following limit: limx-->infinity5x/8x2+5x

A: We find limit  limx-->infinity5^x/8x^2+5^x

Q: lim -2)2 x-2 x2-4 3.)

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Q: Weierstrass's definition of limit to show that lim(x² - 4x+5)= 1. X-2

A: Limit of the function

Q: Evaluate the following limits. If necessary, enter INF for ∞ and -INF for -∞0. a) lim (−2x² + 6) =…

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Q: For each of the limits in parts (a)-(c), determine if the limits exist as a number, as an infinite…

A: We find the limit by using L'Hopital rule and some properties:

Q: Use L' Hopital's Rule if possible, to evaluate the following limits. Show all work, thank you!

A: to find the limits using l'hospital rule where appropriate.