(b) The function 00 f(2) = = + Z- NT n=1 is thus well-defined for every z mm for any integer m. Show that lim zf(z) = 1, f(-z) = -f(2), (2十) = f(). f(/2) = 0, (1) with the middle identities holding whenever either side is defined (z ma for any integer m). Hint: use partial sums for the third equality; the other three are easy.

Q: 3n Find lim,→0 (1+ )'

A: Here,

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A:

Q: . Let (x2 + 1 f(x) = 1( - 2)² if x> 1 if x<1 (a) Find lim,-I- f(x) and lim,→* f(x). (b) Does lim ,1…

A: Given: For (a),     limx→1- f(x)=limx→1 x2+1=12+1=2 and     limx→1+ f(x)=limx→1 x-22=(-1)2 =1

Q: 6. a) State why the limit of f(x) = √5x - 1 does not exist for x

A: Please refer to the image below

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A:

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A: They are solving derivative for v=1w2-1

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A:

Q: 1) Use the graph of f below to estimate the following: m 0 -1+ % 4 a) lim f(x): x-1 b) lim f(x)= c)…

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Q: a f(x)= a. 2x-1 x²-9 3x3 +2x²+3 b. f(x)= x²+3x+2

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Q: 5. Calculate lim f(x), where x+1+ f(x) = = its 12.05 (c)-2 (d) 2 (e) does not exist 5A 5B if x 1 x-1…

A:

Q: x + 1 1x - 122 and use them to determine lim f1x2. Compute the values of f1x2 in the following table…

A: As per given information: x x+1(x-1)2 x x+1(x-1)2 1.1 210 0.9 190 1.01 20100 0.99 19900…

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A:

Q: 5z 3z (a) Evaluate limz-»00

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Q: 10. Calculate (a) 3 (b) 0 (c) 15 lim x⇒1 (d) 13 (e) does not exist x18 - x3 x5 - 1

A: We are required to find the value of : limx→1x18-x3x5-1