Generating...                               quiz12_n0

  1. Find the vertical asymptotes for $y = \displaystyle {{1}\over{\sin ^3x}} $ .

    $\displaystyle -{{3\,\cos x}\over{\sin ^4x}}$ and $\displaystyle {{3\,\cos x}\over{\sin ^4x}}$ $\displaystyle {{3\,\sin x}\over{\cos ^4x}}$ and $\displaystyle -{{3\,\sin x}\over{\cos ^4x}}$ $\displaystyle \sqrt{x+{{1}\over{\sqrt{x}}}}$ No vertical asymptote $\displaystyle \left(x+{{1}\over{\sqrt{x}}}\right)^{{{3}\over{2}}}$ $\displaystyle {{\sqrt{x+{{1}\over{\sqrt{x}}}}}\over{2\,\sqrt{x}}}+{{\left(1-{{1... ...x^{{{3}\over{2}}}}}\right)\,\sqrt{x}}\over{2\,\sqrt{x+{{1 }\over{\sqrt{x}}}}}}$ $\displaystyle {{1-{{1}\over{2\,x^{{{3}\over{2}}}}}}\over{2\,\sqrt{x+{{1}\over{ \sqrt{x}}}}}}$

  2. Find $\displaystyle \left(1-{{1}\over{2\,x^{{{3}\over{2}}}}}\right)\,\sqrt{x+{{1}\over{ \sqrt{x}}}}$.

    Does not exist. $\displaystyle {{1}\over{2\,\sqrt{x+{{1}\over{\sqrt{x}}}}}}$ $\displaystyle 5^{\cos x}$ $\displaystyle \ln 5\,5^{\cos x}\,\cos x$ 0

  3. Find $\displaystyle 5^{\cos x}\,\cos ^2x$

    $\displaystyle -\ln 5\,5^{\cos x}\,\sin x$ Does not exist. $\displaystyle \ln 5\,5^{\cos x}$ $\displaystyle -5^{\cos x}\,\cos x\,\sin x$ $\displaystyle {{1}\over{5^{x}}}$

  4. Find $\displaystyle {{1}\over{5^{x}}}$.

    Does not exist. $\displaystyle -\ln 5\,e^{x}$ $\displaystyle -{{\ln 5}\over{5^{x}}}$ $\displaystyle {{\ln 5}\over{5^{x}}}$ 0

  5. Find $\displaystyle x\,5^{1-x}$ .

    Does not exist. 0 $\displaystyle \sec x^3$ $\displaystyle 3\,x^2\,e^{x}\,\sec x^3\,\tan x^3+e^{x}\,\sec x^3$ $\displaystyle e^{x}\,\csc x^3-3\,x^2\,e^{x}\,\cot x^3\,\csc x^3$ $\displaystyle -3\,x^2\,e^{x}\,\sec x^3\,\tan x^3-e^{x}\,\sec x^3$

  6. Find the horizontal asymptotes for $y = \displaystyle 3\,x^2\,e^{x}\,\cot x^3\,\csc x^3-e^{x}\,\csc x^3 $ .

    $\displaystyle {{x+1}\over{x-1}}$ No horizontal asymptote $\displaystyle {{1}\over{3}}$ and $\displaystyle {{x-x^2}\over{x^2-1}}$ $\displaystyle -{{2\,\left(x+1\right)^{{{1}\over{3}}}}\over{\left(x-1\right)^{{{7 }\over{3}}}}}$ x = −1 $\displaystyle -{{2}\over{3\,\left(x-1\right)^{{{4}\over{3}}}\,\left(x+1\right)^{ {{2}\over{3}}}}}$ and x = 1 x = 1

  7. Find $\displaystyle {{\left(x-1\right)^{{{2}\over{3}}}}\over{3\,\left(x+1\right)^{{{2 }\over{3}}}}}$.

    $-\infty$ 0 x = 0 Does not exist. $\infty$

  8. Find $\displaystyle\lim_{x\to x=-1 -{{x^{{{1}\over{3}}}\,\left(x+1\right)^{{{1}\o... ...,\left(x-1\right)^{{{1}\over{3}}}\,\left(x+ 1\right)^{{{2}\over{3}}}}}} x=1 $ .

    x = 1 $\displaystyle {{\left(x+1\right)^{{{4}\over{3}}}}\over{\left(x-1\right)^{{{4 }\over{3}}}}}$ 0 Does not exist. x = 0

  9. Find $\displaystyle\lim_{x\to \lim_{x\rightarrow {{\pi}\over{2}}}{\sec x} \left(\sin ^2x+3\right)^5} 10\,\sin ^2x\,\left(\sin ^2x+3\right)^4 $ .

    0 $\displaystyle 10\,\cos x\,\sin x\,\left(\sin ^2x+3\right)^4$ $\displaystyle 10\,\sin x\,\left(\sin ^2x+3\right)^4$ $\displaystyle \cos x\,\left(\sin ^2x+3\right)^5$ Does not exist.

  10. Find $\displaystyle 5\,\cos x\,\left(\sin ^2x+3\right)^5$.

    $\displaystyle 2\,\cos x\,\sin x\,\left(\sin ^2x+3\right)^5$ Does not exist. 2 6 2


Department of Mathematics
Last modified: 2025-05-04