1) Suppose r = -32 - 2s 3 with 8 -1. Find ds/dr when 8 = 0 in two w...

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1) Suppose r = -32 - 2s 3 with 8 -1. Find ds/dr when 8 = 0 in two ways: using the Implicit Function Theorem and the formula ds/dr = 1/(dr/ds). and using implicit differentiation 2) Given f(x) = I - 4, find Note: It is useful to observe that f(0) = 3. 3) Give a formula for the derivative = of the function = In²x 4) If f(r) = find P(x) and use this formula to find f"(1). 1+x2 5) A bacteria culture initially contains 1200 cells and grows at a rate proportional to its size. After an hour the population has increased to 2400. (a) Find an expression for the number of bacteria after t hours. (b) When will the population reach 4, 800? Is the answer to b) clear without any computation? How would you answer this if you wanted to reach the population of 9,600 cells? 6) You know that the half life of a radioactive material is 750 years. What is the percent level of radioactivity left after 3,000 years? When will the percent of radioactivity be less than 5% of the original level? 7) When a cold drink is taken from a refrigerator its temperature is 35 degrees Fahrenheit. You sit it on the counter in a large room whose temperature is 75 degrees Fahrenheit. After two hours, the drink's temperature is 55 degrees Fahrenheit. a) What was the temperature of the drink after one hour? b) When will the drink be at 65 degrees Fahrenheit? 8) Consider the function sin Can you use the domain v2function? Give a formula for the derivative of sin -1(1-I2). 9) Compute cosh(In(3)). Is it 3/2, 4/3, or 5/3 ? Or is it something else? 10) Find the derivatives of sinh( and sinh-(Inz). 11) Find a formula for the derivative of tanh(Vi 12) Find the derivative of the following two functions: (1-1(2/(2+1)). 13) Why is it easier to answer the question, "Is cosh(In(2)) > 2?" rather than "ls cosh(2) > 3.5?" 14) Compute lim(1 - using L "Hospital's Rule. =-10 15) Using L'Hospital's Rule, compute the value of lim(coss(r)-cos(3r))/r². 16) Using integration by parts. find Send 17) What is the best way to find (=3(2-1) dr. What is this antiderivative? 18) Using integration by parts, find S=(1+1) 19) Using integration by parts, find Find this integral also using partial fractions. Compare the answers! Why are they the same, up to a constant? 20) Find 21) Find 22) Compute 23) Find 24) Compute 25) Using trigonometric substitution, find fatted 26) Using trigonometric substitution, 27) Using trigonometric substitution, find 6334 2

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