math117_assignment06

# math117_assignment06 - M ath 1 17 Assignment F all 2 008 d...

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1 Math 117 Assignment # (, Fall 2008 due October 30th or 31st Assigned Problems 1. Using the complex forms for the sine and cosine functions, show that (a) cos(8 1 + 8 2 ) = cos 81 cos 8 2 sin 8 1 sin 8 2 (b) cos 2 8 + sin 2 8 = 1 2. Express in the form x + jy: (a) eei (b) sin(5; + j) 3. Given sin(z) = 3, solve for z. 4. Find the values of z = (I - V3j)1/3 . 5. Calculate the complex impedance for the circuit shown below, when a current i{t) = I sin(lOt) passes through the following circuits: L=O.S H R=IOO a C=So. .IO"'F a) A I B b) AOB c= 0.01 F 6. Find f'(x) using the definition of the derivative, where: (a) f(x) = VI + 2x (b) = x4 7. Determine the x and y coordinates of the points where the tangent to x 3 x 2 y( x) = - - X + 1 is horizontal. 8. How many tangent lines to the curve y = x/{x+ 1) pass through the point (1,2)? At which points do these tangent lines touch the curve? 1

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2 9. Differentiate the following functions: (a) v'9~4x (b) V"--xy-x-. .;x-x (c) sin (tan(~») (d) (tan- 1 x)-l () I-F~x~ e l+n x (f) xln(sech4x) 10.
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math117_assignment06 - M ath 1 17 Assignment F all 2 008 d...

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