Integrals of Some Transcendental Functions

March 21, 2008

Evaluate the following integrals:

1. \displaystyle\int \frac{x^2}{1-\cosh^2 (x^3)} \ dx
2. \displaystyle\int 5^x \cot \big( 5^x \big) \ dx
3. \displaystyle\int \frac{dx}{x\sqrt{9x^4-16}}
4. \displaystyle\int\frac{x^2-4x+3}{x^2-4x+5} \ dx

Read the rest of this entry »

2 Comments | Calculus | Tagged: , , , , , | Permalink
Posted by ldvallejo

Logarithmic Differentiation and Derivatives of Some Transcendental Functions

March 21, 2008

Find \frac{dy}{dx}.

1. y = \displaystyle\frac{x^{\sec x} 2^{(x+1)^2}}{x\sin^3 (1+\sqrt{x})}

2. e^{xy} + \cosh^{-1} y = \tan^{-1}(\tanh x)

Read the rest of this entry »

Leave a Comment » | Calculus | Tagged: , , | Permalink
Posted by ldvallejo

Some Limits of Indeterminate Forms

March 21, 2008

Evaluate the following limits:

1. \displaystyle\lim\limits_{x\rightarrow 1} \frac{2x^3-3x^2+1}{3x^3-4x^2-x+2}

2. \displaystyle\lim\limits_{x\rightarrow \infty} \big( xe^{-\frac{1}{x}}-x \big)

3. \displaystyle\lim\limits_{x\rightarrow \infty} \frac{\ln(x+e^x)}{3x}
4. \displaystyle\lim\limits_{x\rightarrow 1^+} (2-x)^{\tan(\frac{\pi}{2} x)}
5. \displaystyle\lim\limits_{x\rightarrow 0^+} \frac{1}{\ln(\cos x)} \int_0^x \tan^{-1} t \ dt

Read the rest of this entry »

4 Comments | Calculus | Tagged: , , | Permalink
Posted by ldvallejo