(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: The limit when x approaches to 5 of a polynomial f(x) is f(-5)

A: Given The limit when x approaches to 5 of a polynomial f(x) is f(-5)

Q: 3n Find lim,→0 (1+ )'

A: Here,

Q: 1 lim (x² –1)sin x+1

A: To find out the limit.

Q: Re Prove directly from definition that it f is a positive function so that lim +(x)=16, then…

A:

Q: (6,5). (1.4) (-4,2), (6,2) -2 6. 8 -2 9(1-2) lim f(z) = I4-4- -4 00 4.

A: Given the above figure. To find limx→-4-f(x)

Q: Suppose that 3- 8x² ≤ g(x) ≤ 3 cos x for all real numbers x. Evaluate: lim g(x) = x-0

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

Q: 3sin(mt) t(6-t) Evaluate lim.→0 where m is a constant

A:

Q: Let 16x-5 1x² +5 Enter the exact value of the one-sided limit lim f(x) 3-2 f(x) = if x ≤ 2 if x > 2

A:

Q: Prove positive function so that lim + (x)=16, then lim√(x)=4 directly from definition that it f is a…

A: Given that Let  f is a positive function so that  limx→-4f(x)=16  .

Q: -2x-8 x - 4 (ь) lim O 0° O 100 O c0 O o.00 O c0 - 00 O not indeterminate

A: Given,  limx→∞x2-2x-8x-4  We have to find the form of the limit.

Q: 4х — 1 4x2 + 3x Find lim f(x) if 5.

A: 4x-1x&lt;fx&lt;4x2+3xx2  for all x&gt;5 Now, limx→∞4x-1x=limx→∞4xx-1x=limx→∞4-1x=4-0=4 &amp;…

Q: Let f be entire and suppose that lim 80+z f(z) Z = 0. Show that f is constant.

A: The given problem is to show that if limz→∞f(z)/z = 0 for the entire function f(z), then f(z) is…

Q: 11. Consider the function f(x) = x³-ax²-x+b X+1 lim f(x) exists, determine all value(s) of lim f(x).…

A:

Q: (M1.4 C) Consider the two functions h(x) = %3D and k(x) 2² + 4x+4 2+x-2 Compute the lim h(x) and lim…

A: Given: The functions hx=x2+x-2x2+4x+4 and kx=x2+4x+4x2+x-2 To find: limx→-2hx and limx→-2kx

Q: 4х — 1 4x2 + 3x - Find lim f(x) if 5. x2

A:

Q: Expand the function p (z + h) as follows. p (z + h) = V(w+h)²–1 Substitute the function p (z + h) in…

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

Q: Use the Squeeze Theorem to show that lim x2 co X-0 cos(207TX) = 0. Illustrate by graphing the…

A:

Q: Q1: lim,»1 x(1 – cos-)

A: Evaluate: limx→1 x1-cos1x

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)…

A:

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

A: The given function is, .The line  is a vertical asymptote of the function , if the limit of the…

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…

Q: For which value of n, does the lim- -ny'+16n = 2 y-2 32-ys

A:

Q: If f is C2 on an interval prove that f(2 + k) – 2/(2) + {(z =A) = r"(2). - lim h-0 h2 = f"(x). The…

A:

Q: Q.2 Show that r(ax) _ 1 lim x0 (x)

A: to show  limx→0ΓaxΓx=1a   ...i as we know Γn=Γn+1n using this formula we get Γx=Γx+1xΓax=Γax+1ax

Q: 5z 3z (a) Evaluate limz-»00

A: Limit of a function is a value obtained when the variable in a function approaches to some other…

Q: The function h is defined by h(x) following statements must be true? A (В B (C) D lim h(x) x→4- lim…

A:

Q: lim (x + 5)(2x + 5) 1) (x – 2) (b) x → * (3x + ·

A:

Q: If (5 – 2a2) < f(x)< (5 – 2²) for -1 <r< 1, find lim,of(x).

A:

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