CALCULUS I TEST #1 SOLUTIONS |
Time limit:
Instructions:
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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 |
4) x² + 4 m 4x x² - 4x + 4 m 0 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)
b) c) |
6)
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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