Recent questions in Calculus 1

Exponential models

Derivatives

Derivatives

Derivatives

Find the four second partial derivatives of $$f(x,y)=x^{2}\sin y$$

Exponential models

Derivatives

Derivatives

Derivatives

Calculate the derivatives of all orders: $$\displaystyle{f}'{\left({x}\right)},{f}{''}{\left({x}\right)},{f}{'''}{\left({x}\right)},{{f}^{{{4}}}{\left({x}\right)}},\ldots{{f}^{{{n}}}{\left({x}\right)}},\ldots{f{{\left({x}\right)}}}={e}^{{{2}{x}}}$$

Exponential models

The exponential growth models describe the population of the indicated country, A, in millions, t years after 2006. Canada $$A=33.1e0.009t$$ Uganda $$A=28.2e0.034t$$ use this information to determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. By 2009, the models indicate that Canada's population will exceed Uganda's by approximately 2.8 million.

Rational functions

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. $$\displaystyle\lim{x}→∞\frac{{{x}−{3}}}{{\sqrt{{4}{x}^{{2}}+{25}}}}$$

Exponential models

Derivatives

Derivatives

Derivatives

Derivatives

Calculate the derivatives of the functions. $$\displaystyle{f{{\left({x}\right)}}}={\left({4}{x}-{1}\right)}^{{-{1}}}$$

Rational functions

Determine the domains of the given rational functions. $$\displaystyle\frac{{{x}^{{2}}-{9}}}{{{x}^{{3}}-{x}}}$$

Exponential models

Derivatives

Calculate the derivatives of all orders: $$\displaystyle{f}'{\left({x}\right)},{f}{''}{\left({x}\right)},{f}{'''}{\left({x}\right)},{{f}^{{{4}}}{\left({x}\right)}},\ldots{{f}^{{{n}}}{\left({x}\right)}},\ldots{f{{\left({x}\right)}}}={x}^{{{4}}}+{x}^{{{3}}}$$

Exponential models