to. 6. The initial population in a bacteria colony is 10,000. After t hours, the colony has grown to a number P(t) given by P(t) = 10,000(1+0.86t +t²) A. Find the rate of change of the population P with respect to time. This is also known as growth rate. B. Find the number of bacteria present after 5 hours. C. Find the growth rate when t = 5. A company determines that the monthly sales S, in thousands of dollars, after t months o

Q: find the transition points, intervals of increase/decrease, concavity, and asymptotic behavior. Then...

A:

Q: 35. Triangular plate Calculate the fluid force on one side of the plate in Example 6 using the coord...

A: The fluid force is calculated by the formula, where a and b is the limit of the plates between whic...

Q: need help

A: Consider the figure below. Let x be the distance between the man and the pole and y be the distance...

Q: Use the Ratio Test to determine whether the series is convergent or divergent. (-8)" n2 n = 1 Identi...

A:

Q: 2550 In(y) Find the derivative of f (y) Enclose arguments of functions, numerators, and denominators...

A: Given function

Q: Determine and justify whether the series is convergent or divergent.

A:

Q: Using Integral Tables Use the table of integrals at the back of the book to evaluate the inte- grals...

A:    

Q: f(x)= (ex+2 +1/e-x -14ex+1) / (xex-ex/x+1 +lnee^x) differentiate?

A:

Q: Find the exact curve x = (y4/8) + (1/4y2), 1 ≤ y ≤ 2

A: First we find the graph of the function in the given region with the help of some points:   In the n...

Q: dy x2 + y2 if dx Find at (x, y) = (5, 6) and z? dz dt = 9 and = 7. dt dt dz dt Additional Materials

A: To determine the derivative.

Q: A student forgot the Product Rule for differentiation and made the mistake of thinking that (fg)' = ...

A:

Q: 18. Show that Vxª + x and Vx* x→o by showing that they both grow at the same rate as x² as x' grow a...

A:

Q: Find the direction of maximum decrease of the function f(x, y, z) =exyz at the point P(1,1,1) and th...

A: Given function is  

Q: 10. True, or false? As x→0, - (4) b. a. x + 3 = (4) d. 2 + cos x O(2) c. f. xln x = 0(xr²) e. e + x ...

A: Let f(x) and g(x) are the real valued function, both defined on some unbounded subset of the real po...

Q: Prove that f (x) = x4 + 5x3 + 4x has no root c satisfying c > 0. Hint: Note that x = 0 is a root ...

A:

Q: Find the equation of the tangent line to the graph of the function f (x) = v 4,4 + 12 at the point (...

A: Consider the equation 

Q: Sketch the graph of f(x) = 18(x – 3)(x – 1)2/3 using the formulas 30(x – 2) 20(x – 2) (x – 1)4/3 f'(...

A:

Q: 23. a. Suppose you have three different algorithms for solving the same problem and each algorithm t...

A:

Q: find the transition points, intervals of increase/decrease, concavity, and asymptotic behavior. Then...

A: y=x5+5x differentiating it w.r.t. x, y'=5x4+5 for critical point,  y'=5x4+5=0 this gives, x=(-1)1/4 ...

Q: find sech Vi tanh Vi dt 49. `csch (In t) coth (n t) dt 50. Vi cln4 •In 2 coth x dx 51. 52. tanh 2x d...

A:

Q: Give an example of a rational function.

A: Rational function : A fraction which has the property that both its numerator and denominator are po...

Q: Please answer part d

A:

Q: OF CHANGE 1. The management of the Titan Tire Company has detemined that the weekly demand function ...

A: If you want any specific question to be answered, then please submit that question only or specify t...

Q: 5. Which of the following functions grow faster than In x as x →o? Which grow at the same rate as In...

A: Hey, since there are multiple subparts posted, we will answer the first 3 subparts. If you want any ...

Q: In Exercises 9–16, express the integrand as a sum of partial fractions and evaluate the integrals. d...

A:

Q: 7. Rewrite the repeating decimal number 0.123123123123... as the sum of a geometric series, then fin...

A:

Q: Describe a way of showing that a continuous function on an open interval (a, b) has a minimum value.

A:

Q: Find h'(-2) if h = f • g, f(x) = -6x2 – 4 and the equation of the tangent line of g at -2 is y = -9x...

A: Slope of y=-9x+6 is = -9 This line is tangent to g at x=-2  So we get: g'(-2)= -9   The tangent line...

Q: Use the Ratio Test to determine whether the series is convergent or divergent. 2(-1)n - 1_3" 2"n3 n ...

A:

Q: where m, n Evaluate lim X/2 cos nx +0 are integers.

A:

Q: What is the slope of the line y = −4x − 9?

A:

Q: 17. Find the volume of the given circular frustum of height h and radii a and b.

A:

Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable.

A: Find the derivative of the function,

Q: What are the horizontal asymptotes of the function in Figure 6? %2F y= f(x) -20 20 40 60 80 FIGURE 6

A: A horizontal asymptote for a function is defined as a horizontal line that the graph of the function...

Q: Find the area of the region inside one leaf of the polar graph: r = sin4x

A:

Q: determine the intervals on which the function is concave up or down and find the points of inflectio...

A:

Q: Prove the following limit formula for e: e = lim (1+x)!/x

A:

Q: What is the fourth derivative? x^12+1

A:

Q: Find two positive real numbers x and y such that their product is 800 and x + 2y is as small as poss...

A: Given that, We have to minimize:

Q: What are the two ways of writing the difference quotient?

A:

Q: find the minimum and maximum value of the function on. the given interval by comparing values at the...

A: Given function: For critical points:

Q: Question number 8

A: Given,  

Q: Tutorial Exercise Use the given transformation to evaluate the given integral, where R is the triang...

A: To determine the Jacobian of the transformation.

Q: 2. Find an interval where f,(x) = sin2 x and f2(x) = cos² x are linearly independent. %3D

A: W(π/4) = -sin(π/2) = -1 W(π/6) = -sin(π/3) = - √3/2 Since, Wronskian is not zero for a single value ...

Q: Determine whether the series is convergent or divergent. If it is convergent, find its sum. бn Σ (1+...

A:

Q: Find two positive real numbers such that the sum of the first number squared and the second number i...

A:

Q: Find the derivative of f(x)   f(x)= (x^2(x^2+1)) / (x^2-1)

A:

Q: to evaluate the integrals in Exercises 77–80. Express your answers in terms of x. sin¬' x dx 77. tan...

A:    

Q: Find the area inside one leaf of the polar graph: r = 3cos3x

A:

Q: Find the minimum value of f (x) = x^x for x > 0.

A: