#$&* course Mth 279 q1Question: `q001. Find the first and second derivatives of the following functions:
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Given Solution: &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating: OK ********************************************* Question: `q002. Sketch a graph of the function y = 3 sin(4 t + 2). Don't use a graphing calculator, use what you know about graphing. Make your best attempt, and describe both your thinking and your graph. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The coefficient of 3 is the altitude of the sine curve. The 4 and 2 inside the parenthesis shift the curve. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I do not know exactly how the 4 and 2 shift the graph.
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Given Solution: &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating: OK ********************************************* Question: `q004. Find the indefinite integral of each of the following: f(t) = e^(-3 t) x(t) = 2 sin( 4 pi t + pi/4) y(t) = 1 / (3 x + 2) YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The integral of a function is just the antiderivative. A constant C must be added because it is an indefinite integral. -1/3 e^(-3t) + C -2cos(4pi t + pi/4) + C (Values from chain rule cancel) Integral of 1/x = ln(x) o (1/3)ln(3t+2) + C confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating: OK ********************************************* Question: `q005. Find an antiderivative of each of the following, subject to the given conditions: f(t) = e^(-3 t), subject to the condition that when t = 0 the value of the antiderivative is 2. x(t) = 2 sin( 4 pi t + pi/4), subject to the condition that when t = 1/8 the value of the antiderivative is 2 pi. y(t) = 1 / (3 t + 2), subject to the condition that the limiting value of the antiderivative, as t approaches infinity, is -1. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: These solutions will allow us to find the value of C. -1/3 e^(-3(0)) + C = 2 o -1/3(1) + C = 2 C = 7/3 -2cos(4pi t + pi/4) + C (Values from chain rule cancel) o -2cos(4pi (1/8) + pi/4) + C = 2pi C = 8.3 Integral of 1/x = ln(x) o (1/3)ln(3t+2) + C o confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): Limits are not my strong suit.
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Given Solution: &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I cant quite remember this formula ------------------------------------------------ Self-critique rating: OK ********************************************* Question: `q007. The graph of a function f(x) contains the point (2, 5). So the value of f(2) is 5. At the point (2, 5) the slope of the tangent line to the graph is .5. What is your best estimate, based on only this information, of the value of f(2.4)? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Would this be linearization?
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Given Solution: &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: `q008. The graph of a function g(t) contains the points (3, 4), (3.2, 4.4) and (3.4, 4.5). What is your best estimate of the value of g ' (3), where the ' represents the derivative with respect to t? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The average slope can be found by the rise over run. .5/.4 = 1.25.
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Given Solution: &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I am confused about how to find the equation for the slope so that I can find the value. ------------------------------------------------ Self-critique rating: " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!