Question

Find the following limits or state that they do not exist. lim_{hrightarrow0}frac{3}{sqrt{16+3h}+4}

Limits and continuity
ANSWERED
asked 2021-03-04
Find the following limits or state that they do not exist.
\(\lim_{h\rightarrow0}\frac{3}{\sqrt{16+3h}+4}\)

Answers (1)

2021-03-05
Evaluate:
\(\lim_{h\rightarrow0}\frac{3}{\sqrt{16+3h}+4}\)
Consider the given expression: \(\lim_{h\rightarrow0}\frac{3}{\sqrt{16+3h}+4}\)
\(=\frac{3}{\sqrt{16+3\cdot0}+4}\)
\(=\frac{3}{\sqrt{16}+14}\)
\(=\frac{3}{4+4}\)
\(=\frac{3}{8}\)
Hence,\(\lim_{h\rightarrow0}\frac{3}{\sqrt{16+3h}+4}=\frac{3}{8}\)
0
 
Best answer

expert advice

Need a better answer?

Relevant Questions

asked 2021-02-25
Find the following limits or state that they do not exist. \(\lim_{x\rightarrow4}\frac{31x-42\cdot\sqrt{x+5}}{3-\sqrt{x+5}}\)
asked 2021-05-27
a) Using limit rules each of the following limits
\(\lim_{x\rightarrow0}\frac{x+1}{x}\)
\(\lim_{x\rightarrow0}\frac{x+1}{x^{2}}\)
\(\lim_{x\rightarrow0}\frac{x}{x+1}\)
\(\lim_{x\rightarrow0}\frac{x+1}{x+2}\)
b) Using limit rules evaluate \(\lim_{x\rightarrow2}\frac{\sqrt{x+7}-3}{x-2}\)
asked 2020-11-23
Find the following limits or state that they do not exist. \(\lim_{w\rightarrow1}\frac{a\cdot1}{(w^2-2)}-\frac{1}{(w-1)b}\)
asked 2020-12-05
Evaluate the following limits or determine that they do not exist.
\(\lim_{(x,y,z)\rightarrow(2,2,3)}\frac{x^2z-3x^2-y^2z+3y^2}{xz-3x-yz+3y}\)
asked 2021-05-02
Find the limit, if it exists. (If an answer does not exist, enter DNE.)
\(\lim\arctan(e^{x})\)
\(x\approx\infty\)
asked 2021-05-28
Verify, using the definition of convergence of a sequence, that the following sequences converge to the proposed limit.
a) \(\lim \frac{2n+1}{5n+4}=\frac{2}{5}\)
b) \(\lim \frac{2n^3}{n^3+3}=0\)
c) \(\lim \frac{\sin (n^2)}{\sqrt[3]{n}}\)
asked 2020-10-19
Determine the limits if they exist: \(\lim_{(x,y)\rightarrow(2,4)}\frac{(x-2)^2(y-4)^2}{(x-2)^3+(y-4)^3}\)
asked 2021-05-22
Find the limit and discuss the continuity of the function. \(\displaystyle\lim_{{{x},{y},{z}}}\rightarrow{\left({1},{3},{4}\right)}\sqrt{{{\left({x}+{y}+{z}\right)}}}\)
asked 2020-11-22
Compute the following limits if they exist \(\lim_{x\rightarrow0}\frac{\sec x-1}{x^3}\)
asked 2021-06-13
The process by which we determine limits of rational functions applies equally well to ratios containing noninteger or negative powers of x: Divide numerator and denominator by the highest power of x in the denominator and proceed from there. Find the limits.
\(\displaystyle\lim_{{{x}\rightarrow-\infty}}{\frac{{\sqrt{{{3}}}{\left\lbrace{x}\right\rbrace}-{5}{x}+{3}}}{{{2}{x}+{x}^{{{\frac{{{2}}}{{{3}}}}}}-{4}}}}\)
...