Suppose lim f(x) = L and lim g(x) = M. Prove that lim [f(x)-g(x)] =L-M. Xa X-a Begin by writing lim [f(x)- g(x)] as a sum. X-a lim [f(x)-g(x)] = lim [f(x) + (g(x)] %3D X-a Xa

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: which of the following expressions is equivalent to: 3cot^2(t)/csc(t)   a. 3-3cos^2(t)/cos(t) b.…

A: This question is related to trignometry, We will solve it using trignometric identities.

Q: 6. Consider the function f Cx)=5(o+5)-25 if X#し if xfO D.IS fCx) continuous at X-0? EXPlain

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Q: x – 1 is X +2 The rang of f(x)= y = ,

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

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Q: Let f(x) = x/² for x0. show that lim f(x)=lim f(x)= too X-50+

A: Find the limits with the psoitive and negative values.

Q: Suppose lim f(x) = L and lim g(x) M. Prove that lim [f(x) - g(x)] = L- M. Xa Xa Begin by writing lim…

A:

Q: Suppose lim f(x) = = x→2 1/2 4 -5, find lim x→2 x²| ƒ(x) + 6 x - 1

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Q: lim f(x) vs f(-3) а. x--3 b. lim f(x) vs f(-1) x--1 c. lim f(x) vs f(1) X-1 d. lim f(x) vs f(3) X-3…

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Q: Show that lim(x+¹)=e².

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Q: a. Evaluate limx→5 f(x), where f(x) = { 11x+ (2 +77) Ef x5 f(x) exists.

A: solution is given below..

Q: 1 Let f(x) = 1, 0sx<2 -x2 + 4x- 3, x22 . Compute lim f(x).

A: Topic -limits

Q: Show by example that lim[f(x) +g(x)] can exist even if lim f(x) and lim g(x) do not exist.

A: Let,  f(x)=1x-c, g(x)=1c-x

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A: Givenf(x)=x a=1To findlimh→0f(a+h)-f(a)h

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A:

Q: [3 3. Consider f (x) =- 2х - 3 if x< 0 Find lim f(x) if x20.

A: To determine the limit of the function.

Q: f²(x) x-2x³-f(x)* 2. Suppose that limf(x) = 5. Compute lim x-2

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Q: e-7x - 2e3 et f (x) = e- *+16e10* + 2e-4z

A: (a) Consider the provided limit, limx→-∞e-7x-2e3x-exe-x+16e10x+2e-4x Evaluate the provided limit.…

Q: lim f(x) = 3 ; im g(x) = 12; lim f(x) = -3 X-->c 4 X->C Xー>C

A: Given;- limx→cfx=34, limx→cgx=12, limx→chx=-3 limx→akfx=klimx→afx lim  x→afx-gx=limx→afx-limx→agx…