CALCULUS I TEST #1 SOLUTIONS

Time limit:

2 hours

Instructions:

No graphing calculators
No notes or crib sheets allowed

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Show all work. Write neatly and big enough to see!!
Numbers in parentheses ( ) are mark values.

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A/ Solve these Inequalities:

 1) multiply by 10 15 < 2 - 8x < 35 transpose the 2 13 < - 8x < 33 divide by -8 Solution: -33/8 < x < -13/8 2) | 6x - 7 | > 1 greater than is 2 separate intervals 6x - 7 < -1 and 6x - 7 > 1 solving the 2 inequalities Solution: x < 1 or x > 4/3.

 3) the zeros are x = -5, 1/3, or 7/5 test the fraction's sign in these intervals, Solution: -5 < x < 1/3 or x > 7/5 4) x² + 4 m 4xx² - 4x + 4 m 0 which makes (x - 2) 2 m 0 which is true for all real numbers since perfect squares are all positive or zero.Solution: x ` ·

(12)

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B/ Evaluate the Limits:

 1) 2) Now invert and multiply, apply limit = -9 3) 4) by the theorem, since n is odd, limit = - º 5) a) b) c) 6) a) b) c)

(18)

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C/ 1) Differentiate. Do not simplify beyond basic algebra.

 a) f '(x) = 3(x 5 - 7x 2)2 (5x 4 - 14x)(3x 4 + 5x) 2 + 2 (3x 4 + 5x)(12x 3 + 5)(x 5 - 7x 2) 3 . b) c) f ' (x) = -15(cot 2 5x)(csc 2 5x)(sec 3x) + 3 sec 3x tan 3x cot 3 5x. d)

(16)

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2) Since the slope of the line 5x - 2y -1 = 0 is 5/2, the derivative must = 5/2
So we know the slope of our tangent. We must find the point of contact.
The derivative y ' = 6x + 4 so we set 6x + 4 = 5/2 and solve for x.
We find x = -1/4 which makes y = -109/16.
We write the equation of the line through this point with slope = 5/2.
Solution: 5x - 2y - 99/8 = 0

(4)

TOTAL (50)

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