Solved Problems in Calculus - Page 2

Problem 2-5: Evaluating Indeterminate Form

Posted on April 9, 2010 by Dr. Yaz Z. Li

Calculate $\displaystyle\lim_{x\to 2}\frac{\sqrt{x+2}-2}{x-2}$ .

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Posted in Limits | Tagged indeterminate form | 2 Comments

Problem 2-4: Computing Limits of a Rational Function

Posted on April 9, 2010 by Dr. Yaz Z. Li

Compute
a) $\displaystyle\lim_{x\to 3}\frac{x^2+2x-3}{x+3}$
b) $\displaystyle\lim_{x\to -3}\frac{x^2+2x-3}{x+3}$

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Problem 2-3: Solving an Inequality

Posted on April 9, 2010 by Dr. Yaz Z. Li

Solve the inequality $|2-3x|<3$ .

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Posted in Precalculus | Tagged inequality | 2 Comments

Problem 2-2: Evaluating Derivative of Functions and the Tangent Lines

Posted on April 7, 2010 by Dr. Yaz Z. Li

Find the derivative of $f(x)$ and the equation of the tangent line at $x_0=-1$ .

a) $f(x)=x^2$
b) $f(x)=x^3+x+1$
c) $f(x)=\frac{1}{x}$

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Problem 2-1: Linearity of Functions

Posted on April 5, 2010 by Dr. Yaz Z. Li

Which one(s) of the following functions is linear?

a) $y=x+1$ .
b) $y=2x+1$ .
c) $y=1$ .
d) $y=x^2+x+1$ .
e) $y=x^1+1$ .
f) $y=\frac{1}{x}$ .
g) $y=\sin(x)$ .
h) $y=\sqrt{x}$ .
i) $y=x+\frac{1}{1-x}$ .
j) $5x+2y-1=0$ .
k) $y=x+c^2$ . ( $c$ is an arbitrary constant).

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Posted in Precalculus | Tagged function, linear, linear function | Leave a comment