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Recent questions in Calculus and Analysis
First order differential equations
ANSWERED
asked 2021-07-05
Write first-order differential equations that express the situation: The increase in the number of people who have heard a rumor in a town of population 20,00020,000 is proportional to the product of the number PP who have heard the rumor and the number who have not heard the rumor at time tt .
Derivatives
ANSWERED
asked 2021-07-05
Find the derivatives of the functions.
\(\displaystyle{t}{\left({x}\right)}={4}^{{-{x}+{5}}}\)
Derivatives
ANSWERED
asked 2021-07-05
Find the derivatives of the functions.
\(\displaystyle{s}{\left({x}\right)}={\ln{\sqrt{{{\ln{{x}}}}}}}\)
Differential equations
ANSWERED
asked 2021-07-05
\(\displaystyle{y}'={\left({y}+{4}{x}\right)}^{{2}}\)
Derivatives
ANSWERED
asked 2021-07-04
Find the derivatives of the functions.
\(\displaystyle{h}{\left({x}\right)}={\ln{{\left({\frac{{{y}_{{{x}}}}}{{{4}{x}-{2}}}}\right)}}}\)
Derivatives
ANSWERED
asked 2021-07-04
Find derivatives of the functions defined as follows.
\(\displaystyle{y}=-{4}{e}^{{-{0.3}{x}}}\)
Derivatives
ANSWERED
asked 2021-07-03
Find the derivatives of the functions.
\(\displaystyle{f{{\left({x}\right)}}}={\left({\ln}{\left|{x}\right|}\right)}^{{{2}}}\)
Derivatives
ANSWERED
asked 2021-07-03
Find the derivatives of y with respect to the appropriate variable.
\(\displaystyle{y}={x}{{\sin}^{{-{1}}}{x}}+\sqrt{{{1}}}={x}^{{{2}}}\)
Derivatives
ANSWERED
asked 2021-07-01
Find derivatives for the functions. Assume a, b, c, and k are constants.
\(\displaystyle{g{{\left({x}\right)}}}={2}{x}-{\frac{{{1}}}{{\sqrt{{{3}}}{\left\lbrace{x}\right\rbrace}}}}+{3}^{{{x}}}-{e}\)
Derivatives
ANSWERED
asked 2021-06-30
Find the derivatives of the given functions.
\(\displaystyle{h}{\left({x}\right)}={2}{\sec{{x}}}+{3}{\tan{{x}}}+{3}{x}\)
Derivatives
ANSWERED
asked 2021-06-30
Find derivatives of the functions defined as follows.
\(\displaystyle{y}={e}^{{{4}{x}}}\)
Derivatives
ANSWERED
asked 2021-06-29
Find derivatives for the functions. Assume a, b, c, and k are constants.
\(y=17x+24x^{1x2F2}\)
Limits and continuity
ANSWERED
asked 2021-06-28
Find the limit (if it exists) and discuss the continuity of the function.
\(\displaystyle\lim_{{{x},{y}}}\rightarrow{\left({1},{1}\right)}{\frac{{{x}{y}}}{{{x}²+{y}²}}}\)
Derivatives
ANSWERED
asked 2021-06-27
Find the derivatives of the functions.
\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{\ln}{\left|{x}\right|}}}}\)
Derivatives
ANSWERED
asked 2021-06-27
Find derivatives for the functions. Assume a, b, c, and k are constants.
\(\displaystyle{j}{\left({x}\right)}={\ln{{\left({e}^{{{a}{x}}}+{b}\right)}}}\)
Limits and continuity
ANSWERED
asked 2021-06-26
Find the limit and discuss the continuity of the function.
\(\displaystyle\lim_{{{x},{y}}}\rightarrow{\left({\frac{{\pi}}{{{4}}}},{2}\right)}{y}{\cos{{x}}}{y}\)
Derivatives
ANSWERED
asked 2021-06-26
Find the derivatives of the functions.
\(\displaystyle{g{{\left({x}\right)}}}={e}^{{{3}{x}-{1}}}{e}^{{{x}-{2}}}{e}^{{{x}}}\)
Derivatives
ANSWERED
asked 2021-06-26
Calculate the derivatives of all orders:
\(\displaystyle{f}′{\left({x}\right)},{f}{''}{\left({x}\right)},{f}{'''}{\left({x}\right)},{{f}^{{{4}}}{\left({x}\right)}},\ldots,{{f}^{{{n}}}{\left({x}\right)}},\ldots{f{{\left({x}\right)}}}−{4}{x}^{{{2}}}−{x}+{1}\)
Derivatives
ANSWERED
asked 2021-06-26
Find the derivatives of the given functions.
\(\displaystyle{f{{\left({x}\right)}}}={\sin{{\left({3}{x}-{5}\right)}}}\)
Multivariable functions
ANSWERED
asked 2021-06-26
Let
\(\displaystyle{f{{\left({x}\right)}}}={5}⋅{2}^{{x}}\)
a. Write an equation for p, the parent function of f.
b. Give the equation for an asymptote of both p and f.
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