Show directly from definitions that if f(x) and g(x) are real func- tions, bounded on [0,1], and so that lim f(x) = 2 and lim g(x) 3, then 2-04 lim f(x) g(x) = 6. 2-40+ -

Q: If f(x) is defined by the following ²-16 =x2-4 2-3x-1 Let f(x) x> 2 *<2 Then find the lim f(x) & lim…

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Q: (b) Assume that lim,6 f(r) = 9 and that lim,6 g(r) = 3. Compute lim f(r)g(r) - f (x)f(x) + g(x)g(x)

A: To Determine: The given expression:

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

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Q: * +3 ,x1 „x>1 g(x) exists? Justify. 1+1 f(x) a) Does lim f(x) + g(x) exists? Justify. b) Does lim

A: Solve the given function

Q: а) If V5 - 2r s f(x)s V5 – x² for -1sxsl Find lim,o f (x) ?

A: Given that                                5-2x2≤f(x)≤5-x2  for  -1≤x≤1 we have to find…

Q: Find the lim f(x) if, for all x > 11, 7x-1 < f(x) < 7x + 5x x2

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Q: find the Lineartransfromation T:Maxz (R) /R whose matrix MT with vegard tothe base and the base…

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Q: Find the lim inf (xn) and lim sup (xn) of Xn=3-(-1)"

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Q: Asap

A: Let's evaluate limits.

Q: USE SQUEEZE Theorem do poho Lim I'm x² esin(x) и х 0+X

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Q: x2 – 4, x 3 -

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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

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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: Let g(x) and h(X) be functions with lim g (x) = G and lim h (x) = Hwhere G and H are real numbers.…

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Q: Find the lim f(x) if, for all x > 13, 7x – 3 < fx) < 7x² + 4x

A: Given : 7x-3x &lt; fx &lt; 7x2+4xx2

Q: Find lim f(x) if x →∞ 4x - 1 X f(x) 5.

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Q: Given the function f(x) = Which f the following is/are true? (x- 1)(x + 1) 1. lim f(x) = +00 2-1+ 2.…

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

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

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Q: Find lim f(x) and lim f(x) for I-2 x² + 2x I < -2 Vr + 2 4x – 2 2<I f(x) = -2 < x < 2 -

A: Topic- limits

Q: 2. Consider f(x)=x² – 4x + 2 a) lim f(x) x-2 b) lim f(x) x-4 c) lim f(x) We X-1

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Q: if x1 then lim,-1 f(x) is 3 if x 1 (b) 3 3. Let f(x) = (a) 1 (c) not exist (d) other

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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: If lim x→0 a) f(x) x = 1 and lim x-0 lim g(x) x→0 g(x) – 2, evaluate: X b) lim x-0 g(x) f(x)

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: :-√√3x lim x-3 27-x3

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find all values of a and b that make -a - x, x< -2 /(x) = { Vx + b, bx² + 1, -2 Sx<1 x21 continuous…

A: Given:             fx=-a-x,            x&lt;-2bx2+1,    -2≤x&lt;1x+b,        x≥1