lim f(x): = lim f(x) = LE R. Let f = C(-∞, +∞), and x-x Prove: f(x) is bounded in R. 8+←8

Q: 2) Evaluate the limit at x=1 for: x* + 7x2 – x – 2 f(x) x² – 5x + 4

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Q: Show that lim Z-2 (2-2)4 || ∞

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Q: f(x): = ax² + x - b, ax + b, 2ax - 7, (a) Find the values of a and b such that f is continuous on…

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Q: 2 1 lim х->1| х — 1 X→1 X - 1

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Q: C Lim x+h -rx , hto. H.. h.

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Q: x² – 9 (b) lim x→3- x + 3

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Q: 0- V5 – x – V5+: -

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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: lim t→∞ 14/3 + 71/3 2 (6+²/3 +11) ²

A: To find out the limit.

Q: Find the limits in Exercise

A: Given: Let y=limt→6 8t-5t-7  To Find: To evaluate the given limit.

Q: Consider the function f(x) = {,* - a, -1<x< 2 lb – 2x, 2<x<4 If b =1 and the limit of f (æ) as æ → 2…

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Q: Let f be a function with continuous f" such that f(3) = 0, f'(3) = 2, and f"(3) = –1. Evaluate the…

A: use L Hospital Rule to find the given limit.

Q: Show directly from definitions that if f(x) and g(x) are real func- tions, bounded on [0,1], and so…

A: Given: fx and gx are real functions, bounded on [0, 1], and limx→0+fx=2 and limx→0+gx=3 We have to…

Q: Find the limit limx→∞(1+1x)3x.

A: we have to find the limit : limx→∞(1+x)(3x)

Q: p³ + x² – 4 4x = x +1+ - 1. Consider the function f(x) Note that - 4° x² – 4 x2 (x2 – 12) (т? — 4)2…

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Q: lim x-3-j 2 x²-8-j6 2x²− x³ −3l+x −j37

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Q: x²+3x Compute the limit limx→∞ x³+2· -

A: Given limx→∞x2+ 3x-x3 + 2

Q: Let g(t) : 3 - VE t – 9 - Find the value of lim_9 g(t), or state that it does not exist.

A: g(t)=3-tt-9

Q: Find the limit of lim x(√64x²5 ∞0++* √64x²14) = = lim x(√64x²5 -5-√√64x²-14) ∞0++x

A: limx→∞x64x2-5-64x2-14

Q: Let f(x) = 3x7 if x < 5 if 755 x ≥ 5 Show that f(x) has a jump discontinuity at x = 5 by calculating…

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