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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. math exams: March 2012

Wednesday, March 28, 2012

Question Calculus 28/03/2012 10:58

\int \! \frac{x^{2}}{\sqrt[4]{x^{3}+2}} \, \mathrm{d} x

Ans \frac{4}{9}({x^{3}+2})^{\frac{3}{4}}+C

Question Calculus 28/03/2012 10:45

\int \! \frac{1}{e^{x}+1} \, \mathrm{d} x

Ans: x-\ln­|e^{x}+1|)+C

Question Calculus 28/03/2012 10:10

\int \! \frac{(1+x)^{2}}{\sqrt{x}} \, \mathrm{d} x

Ans 2x^{\frac{1}{2}}+\frac{4}{3}x^{\frac{3}{2}}+\frac{2}{5}x^{\frac{5}{2}}+C

Question Calculus 28/03/2012 2:05

\int \! \frac{x^{3}}{x+1} \, \mathrm{d} x

Answer \frac{x^{3}}{3}-\frac{x^{2}}{2}+x-\ln(x+1)+C

Question Calculus 28/03/2012 2:02

\int \! \frac{2x-1}{2x+3} \, \mathrm{d} x

Answer x-2\ln(2x+3)+C

Question Calculus 28/03/2012 1:52

\int \! \frac{1}{x^{3}} \, \mathrm{d} x

Answer -\frac{1}{2x^{2}}+C

Monday, March 5, 2012

Question Calculus 5/03/2012 11:15

\lim_{x \to \infty} \frac{x^2x^{\frac{1}{2}} -1}{x^{3}+x^{2}-6}

Answer : 0

Question Calculus 5/03/2012 11:11

\lim_{x \to 3} \frac{6-\frac{18}{x}}{x-3}

Answer : 2

Question Calculus 5/03/2012 10:56

\lim_{x \to 3} \frac{x^2 -9}{2x-6}

Answer : 3