Can you answer the questions clearly ?
A population model is used to describe how the rate of reproduction of organisms depends on the amount of nutrients that are available. The model shows how the rate of division of E. coli cells depends upon the amou depends upon the amount of sugar added to their growth flask. If r is the rate of reproduction (number of divisions in Compute f(c + h) - f(c) at the indicated point. one hour) and C is the amount of glucose sugar added to the growth medium measured in moles, then the following applies. 1.36C (x) = 7x2; c= (C)C+ 0.24 x10-4 (a) Show that the reproduction rate goes to zero when the sugar level is low; that is lim r(C) = 0. (c + h) - f(c) = at c=8. 1.36 (0) Type an expression using h as the variable.) Since r is continuous at C = 0, Jim r(C) = ( 0) = 0 +0.24 x 10-4 (b) Show that if more and more sugar is added, the reproductive rate plateaus; that is, lim r(C) exists and calculate this limit. aim r(C) =(Type an integer or a decimal.) Use the formal definition to find the derivative of g(x) = 15x at x =4. Find g'(x) for the given function. g'(x) = Use the function below to answer parts (a)-(c). f(x) = x" . 5 a) Use the formal definition to find (b) Find 1(2) and find the equation of the tangent line at the point (2, f(2). (c) Graph y = 1(x = f(x) and the tangent line at the point (2. [(2)) in the same coordinate system. (a) Show that y = x", XER, is an even function (b) Show that y =x , XER, is an odd (a) The derivative of a function fat x, denoted by f'(x), is f(x)= lim - provided that the limit exists. Use the definition of the derivative of fat x to find the derivative of the given function f(x) when x = 2 a) A function f : A-+B is called even if f(x) = f(-x) for all xA. -[(2) +5] ((2) = lim Let fix) =x ". Write the expre (-x)" (Do not simplify.) Why is this expression equal to x*? O A. Multiplying the base by itself four times results in a negative expression, which cancels out the negative in front of the entire term. O B. Multiplying the base by itself any number of times results in a positive expression. O C. Multiplying the base by itself any number of times results in an expression with the same sign as the base. D. Multiplying the base by itself four times results in a positive expression. Use the function below to answer parts (a)-(c). (b) A function 1 : A-+B Is (x) = -1( -x) for all XA. f(x ) = Let fix) =x3. Write the ex ation in the previous step. (a) Use the formal definition to find the derivative of y = f(x) atx (b) Find 1(4) and find the equation of the normal line at the point (4, 1(4))- (-x)(Do not simplify.) (c) Graph y = f(x) and the tangent line at the point (4, f(4)) in the same coordinate system. (a) The derivative of a function f at x, denoted by f'(x), is f'(x) = lim - provided that the limit ex h - + 0 to find the derivative of the given function f(x) when x = 4. Find the inverse of the function together with its domain, and graph both functions in the same coordinate system. f' ( 4 ) = lim 1(x) =5%, XER The inverse function of 5" is f"(x)= In (5) In (x) The domain of the inverse function is exactly predict rest The relationship between mammal body mass (M) measured in grams and resting heart rate (R) measured in beats per minute is R(M) = 1180M * . This relationship is to be s (a) through (c) below. (a) Professor R.'s dog Molly weighs 24 kg. Predict Molly's heart rate from the formula for R(M). The heart rate is 95 beats per minute. (Round to the nearest whole number as needed. (D) Professor R. edict his heart rate from the formula for R(M). The heart rate is 71 beats per minute. (Round to the nearest whole number as needed.) (c) In reality, Molly's resting heart rate is about 45 beats per minute, and Professor R.'s heart rate is about 65 beats per minute. Calculate the relative error from using the heart beat formula. The formula for relative error is real heart beat rate - predicted heart beat ratel predicted heart beat rate The relative error for Molly's heart rate is 0.526 (Round to three decimal places as needed.) The relative error for Professor R's heart rate is Round to three decimal places as needed.)
