1. Estimate the value of each of the following limits by constructing appropriate tables of values. Then determine the exact value of the limit by using algebra to simplify the function. Finally, plot each function on an appropriate interval to check your result visually. x²- а. lim bx→1 x-1 (2+x)3-8 b. lim x→0 x+1-1 с. lim bx→0

Q: Determine the following limits. ? lim xS0 4x2 6x V16x* 16x* + + + x*

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Q: 11. If f(x)=Vx f(x)-f(4)| The lim x→4 х-4

A: Given: fx=x To Find:  limx→4fx-f4x-4=?

Q: Evaluate the following limits. If needed, enter inf for and -inf for -0. lim (-33x² +21x³) = A/ 818…

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Q: 4. f(x) = x² – 1; c=-1

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Q: Find Lim A. 00 C. olo x² - 4x x-00 3x³ + 6x 0 B. 0 D. 2 NI3

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Q: Consider the function, f(x) = 3x -4. Write and simplify the difference quotient and Find the limit…

A: It is given that, f(x)=3x-4   Difference quotient is defined as that if a function f(x) is given,…

Q: 5. lim x-0 e2x-1

A: LetL=limx→ 0xe2x-1Plug in the value x=0L=0e2(0)-1L=01-1L=00Therefore Apply L Hospital ruleL=limx→…

Q: Use the given graph to: + + + -4, -3 -2 4 3 0 1 2 3 4 X Find lim f(x). X→

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Q: a. Estimate the value of lim f(x).

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Q: 2. Find the limit of the following functions a. lim (-3x² + 5x – 4) x-18

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

A: Given: limx→5 x2+11-6x2-25

Q: For the function shown below, determine the following: a. limf(x) b. limf(x) ズーラ2 c. lim f(x) d.…

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Q: x-2 22. Evaluate lim x+2 Vx2-4

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Q: Find the lim as h approaches 0 for the given function

A: Given f(x)=x2+5limh→0f(h+4)-f(4)h

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.