2. If lim f(x) = L and lim g(x) = M = 0, find lim x-a x1 x-a f(x) g(x) or explain why DNE. Is x = a a VA of h(x) = f(x)?

Q: (a) lim [f(x) + 3g(x)]

A: Given:  limx→2  fx=1,  limx→2  gx=-2,  limx→2  hx=0 To Find:  limx→2  fx+3gx=?

Q: 3. Sketch a graph of a function y = f(x) that satisfies all of the following (if possible): а. x-0-…

A:

Q: If g(x) is differentiable at x = 1, then lim g(x) = g(1). x+ 1+ True False

A: A function f(x) is differentiable at x=a, if limit exist at x=a and is equal to f(a)

Q: If lim f(x) = 2, and lim g(x) = 7 find: C→C I-C a) lim 4f(z) A C b) lim ln(g(x))

A:

Q: 4. Is it possible that there exists some function g(x) and some constant L such that lim g(x) = lim…

A: First we need to understand definition of limit:

Q: If lim f(x)=-2 and lim g(x) = 2, what is the value of lim [f (x)+2g(x)]?

A: Given, limx→afx=-2  and  limx→agx=2

Q: Use the graphs of f and g and their tangent lines at (-1,0) to find f(x) lim Number x-1 g(x) y f(x)…

A:

Q: Find the slope of the tangent line to the function’s graph at the given point using the definition…

A:

Q: 2 ež h(x) 1 - 4 What is lim h(x)? x→+∞

A:

Q: If 3x − 1 ≤ f(x) ≤ x2 − 3x + 8 for x ≥ 0, find lim x→3 f(x).

A: Here we use sandwich theorem Also known as squeeze theoremThis theorem states that , if gx≤fx≤hx in…

Q: If lim H(h) = x and. lim H(h) = y, then find lim H(h3 -h) %3D h-0- h-0+

A: Given limit expressions are limh→0+Hh=x,limh→0-Hh=y.

Q: The graph of f is given. Use the graph to compute the quantities asked for. (If an answer does not…

A:

Q: 2f(x) ) lim x→2 g(x)

A: Given: Limit equations is given.

Q: If lim as t approaches 4 of the function ((g(x)-6)/(t-1))=1. Find lim t approaches 4 of g(t).

A: The given function is ((g(x) - 6) / (t - 1))  As limit t approaches to 4 the value of the function…