hmwrk 1 - ) ( x x g = , what is the expression for f(g(x))...

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Homework 1 Solutions 1.Find the solutions of 0 21 2 2 = + x x . ) 3 )( 7 2 ( + = x x 0 ) 7 2 ( = + = x and 0 ) 3 ( = x 2 7 , 3 = x 2. If 17 2 ) ( 2 + = x x f , what is the expression for ) ( x f ? Plug x into the equation in place of x to get: 17 2 17 2 ) ( 2 + = + = x x x f 3. What is the derivative with respect to x of x x x x f 2 sin ln ) ( 2 + = ) ( ) ( ) ( v dx d u dx d v u dx d + = + = ) 2 (sin ) ln ( 2 x dx d x x dx d + x x x x x x x u dx d v v dx d u x x dx d ln 2 2 * ln 1 * ) ln ( 2 2 + = + = + = ) 2 cos( 2 ) 2 (sin x x dx d = So, the final equation is ) 2 cos( 2 ln 2 ) 2 sin ln ( 2 x x x x x x x dx d + + = + 4. This problem can be solved be taking the derivative of the numerator and denominator and plugging in the value of x. 0 1 0 1 2 lim 2 0 = = = = x x x x 5. The derivative is zero at the extrema.
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6. If x e x f x 2 tan ) ( = and ) ln(
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Unformatted text preview: ) ( x x g = , what is the expression for f(g(x)) ? Plug g(x) into the equation in place of x and solve. x e x g f x ln tan )) ( ( 2 ln = = x x x g f ln tan )) ( ( 2 = 7. What is the equation of the straight line passing through the points (1,2) and (5,-1)? b mx x y + = ) ( 1 2 1 2 x x y y m − − = 4 3 1 5 2 1 − = − − − = m 4 11 4 3 2 ) 1 ( 4 3 ) ( + − = + − − = + − = x x b a x m y...
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This note was uploaded on 04/28/2008 for the course GEEN 1300 taught by Professor Degrazia,j during the Spring '08 term at Colorado.

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hmwrk 1 - ) ( x x g = , what is the expression for f(g(x))...

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