Determine the interval(s) on which the following functions are continuous. At which finite endpoints of the intervals of continuity is f continuous from the left or continuous from the right? 

f(x)=√25−x^2

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim t→5 (1/t^2 − 4t − 5 −1/ 6(t − 5))

Determine the interval(s) on which the following functions are continuous. At which finite endpoints of the intervals of continuity is f continuous from the left or continuous from the right? 

f(x)=√x^2−3x+2

Sketch the graph of a function with the given properties. You do not need to find a formula for the function. 

f(2) = 1,lim x→2 f(x) = 3

Analyze the following limits and find the vertical asymptotes of f(x) = (x − 5) / (x² − 25).

lim x → -5^- f(x)

Analyze the following limits and find the vertical asymptotes of f(x) =(x − 5) / (x² − 25).

lim x→−5⁺ f(x)

Determine the interval(s) on which the following functions are continuous. At which finite endpoints of the intervals of continuity is f continuous from the left or continuous from the right? 

f(t)=(t^2−1)^3/2

Analyze the following limits and find the vertical asymptotes of f(x) = (x + 7) / (x⁴ − 49x²).

lim x → -7 f(x) 

Analyze the following limits and find the vertical asymptotes of f(x) = (x + 7) / (x⁴ − 49x²).

lim x→0 f(x)

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim h→0 √16 + h − 4 / h

Determine the following limits.​

lim x→−∞ e^x sin x

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim x→4 1/x−1/4 / x − 4

Evaluate each limit. 

lim x→−1 (x^2−4+ 3√x^2−9)

Determine the following limits.​

lim x→1^− x/ ln x

Analyze the following limits. Then sketch a graph of y=tanx with the window [−π,π]×[−10,10]and use your graph to check your work.

lim x→π/2^+ tan x

Analyze the following limits. Then sketch a graph of y=tanx with the window [−π,π]×[−10,10]and use your graph to check your work.

lim x→π/2^− tan x

Analyze the following limits. Then sketch a graph of y=tanx with the window [−π,π]×[−10,10]and use your graph to check your work.

lim x→π/2^+ tan x

Analyze the following limits. Then sketch a graph of y=tanx with the window [−π,π]×[−10,10]and use your graph to check your work.

lim x→π/2^− tan x

Determine the following limits.​

Assume the function g satisfies the inequality 1≤g(x) ≤sin^2 x + 1, for all values of x near 0. Find lim x→0 g(x).

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim h→0 (5 + h)^2 − 25 / h

A function f is even if f(−x)=f(x), for all x in the domain of f. Suppose f is even, with lim x→2^+ f(x)=5 and lim x→2^− f(x)=8. Evaluate the following limits.

a. lim x→−2^+ f(x)

A function f is even if f(−x)=f(x), for all x in the domain of f. Suppose f is even, with lim x→2^+ f(x)=5 and lim x→2^− f(x)=8. Evaluate the following limits.

lim x→−2^− f(x)

Evaluate each limit. 

lim θ→0 (1/(2+sinθ)-1/2)/sin θ

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim x→4 3(x − 4)√x + 5 / 3 − √x + 5

Evaluate each limit. 

lim x→0+ 1−cos^2x / sin x

Evaluate each limit. 

lim x→0 e^4x−1 / e^x−1

Evaluate each limit. 

lim x→e^2 ln^2x−5 ln x+6 lnx−2

Determine the interval(s) on which the following functions are continuous; then analyze the given limits. 

f(x)=csc x;lim x→π/4f (x);lim x→2π^− f(x)

Determine the interval(s) on which the following functions are continuous; then analyze the given limits. 

f(x)=1+sin x / cos x; limx→π/2^− f(x); lim x→4π/3 f(x)

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim t→2+ |2t − 4|t^2 − 4