Question

The number of miligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by

x(t)= 2000t/t^2+16

(a) For what t-values is x increasing?

(b) Find the t-value at which s is maximum.

(c) Fine the maximum value of x.

Tagged in

Math

Calculus

Find answers to questions asked by students like you.

Q: During the first four months of employment, the monthly sales S (in thousands of dollars) for a new ...

A: Part (a)S= S(x)= 9 / x + 10 + x / 4, x ≥ 4The given function is defined only for x ≥ 4. We don't hav...

Q: Please sketch this by hand! And show all your steps as im doing my best to fully understand the proc...

A: (A) The function has an absolute maximum but no local maximum. This means the graph is strictly incr...

Q: How can I get the result? Which is the result?

A: The given function is,

Q: find the derivative of g(x)= 3x3- 2/ square root x you dont need to simplify answer, but use paren...

A: The given function is,

Q: If l0g x=0.35 and fog6N0.5, evaluate the fo llowig expression.

A: Here, we use the above log rules.

Q: If y (x25x-1)e2x then y (3x2-10x+7)e2x O (2.7x+4)e2x O(22+ 12x + 3)e2x (2x+5)32x (2x 52-1

A: Given,

Q: Determine the location and value of the absolute extreme values of f on the given interval, if they ...

A: The function is defined as

Q: 3x4 y‴+9x4 =5xy′+5x5 y″+9lnx Determine the order of the differential equation shown above.

A: The given differential equation is,

Q: y′=3x−2 Find the particular solution to the equation shown above that passes through the point (−10,...

A: Firstly, we separate the variables x and y, and then integrate both sides.

Q: Let R be the region bounded by y x, x 1, and y 0. Use the shell method to find the volume of the sol...

A: (A)It is given that, the region bounded by y = x2, x = 1 and y = 0.The region around the line y = -8...

Q: Marginal Revenue. Suppose the total revenue function for a blender is R(x)= 36x-0.01x2 dollars where...

A: The total revenue function for a blender is R(x)= 36x-0.01x2 dollars where x is the number of units ...

Q: The area of a circle increases at a rate of 3 cm^2 per second. Find a) how fast is the radius changi...

A: Given information:The area of a circle increases at a rate of 3 cm square per second

Q: Logarithmic differentiation

A: The given function is y=(x+1)²(x-2)(x²+3).

Q: find the exact length of the curve of the equation below, show all work y = ln(sec(x)), with a range...

A: First, we find the dy/dx

Q: How does the limiting behavior of solutions depend on the value of y(0)?

A: Given autonomus differential equation:Graph of function f is given.We need to show the the limiting ...

Q: Find y' if x^y = y^x .

A: Given,

Q: A hot-air balloon is 190 ftabove the ground when a motorcycle (traveling in a straight line on a h...

A: Let x be the horizontal distance from balloon to motorcycle, y be the vertical distance from the bal...

Q: find the inverse of y from the function that is in the picture below

A: Giveninformation:The given function is

Q: Help with #8

A: Let's understand the formula for calculation of curvature.For a function, y(x) the curvature is give...

Q: Use Newton's method to approximate all intersection points of the following pair of curves. Round to...

A: Before we get into the solution of the question, let's understand a bit about Newton's method. If xn...

Q: Use any method to determine if the series converges or diverges. Give reasons for your answer.

A: The given series is

Q: approximate the area under the graph of f(x) and above the x-axis using the following methods with n...

A: Given:The function is f(x) = ex-1.The interval (a, b) is (0,1)

Q: lim x→5 f(x) where f(x)= { 7x-10 if x<5; 25 if x>=5

A: To find the limit x->5 f(x), we have to find the right and left limit of x=5 first.

Q: 2. Given the given function f(x) = x+defined on the interval [1, 3], determine if the function satis...

A: The given function is continuous and differentiable on the whole real numbers except zero. In partic...

Q: Find the position and velocity of an object moving along a straight line with the given acceleratio...

A: Obtain the velocity as follows.

Q: k 5k! x Find the radius of convergence of- (2kk The radius of convergence is Type an exact answer in...

A: We have to find radius of convergence of series.Series is given below:

Q: How can I get the result? Which is the result?

A: (a)we are given a function

Q: a. Determine whether the Mean Value Theorem applies to the function f(x)= ex on the given interval [...

A: Definition used: Mean Value Theorem

Q: Determine the radius and interval of convergence of the following power series. к?(- 5)2к k! The rad...

A: Given,

Q: Find the slope of the tangent line to the given polar curve: r = 2 - sin(theta), at theta = (pi/3) s...

A: Click to see the answer

Q: How do I solve the initial value problem using P(x), Q(x) and v(x)?

A: First we find P(t) and Q(t) by comparing with y\'+P(t)y=Q(t).

Q: 1000 Find the marginal cost when q = 10. 9 The average coste for producing q units of a product is g...

A: The average cost c is given by ,

Q: a. find a possible function f and number a b. evaluate the limit by computing f`(a).

A: We first write the given function in the form of the definition of the derivative.

Q: Help me please..

A: The Taylor series for cosx at x=0.

Q: Help with #4

A: Click to see the answer

Q: 18. CCT 11 The quantity (in pounds) of a gourmet ground coffee that is sold by a coffee company at a...

A: The quantity (in pounds) of a gourmet ground coffee sold at the price of p dollars per pound is give...

Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is inf...

A: We first have to factor the numerator and the denominator.

Q: (2x-3)4 dx 10

A: Given:The integral is

Q: :)

A: Given:The given curves are y = x2, x = 1, and y = 0.The volume of the solid revolved around the line...

Q: How can I get the result? Which is the result?

A: Click to see the answer

Q: Which of the following is the power series representation for g(x)? +8 OA. B. k 8 1 k 0 k 0 8k O C. ...

A: Note that the function g(x) is not provided (here option (c) can also be a power series). So, we are...

Q: The rectangular coordinates of a point are given. Find polar coordinates of the point. Express 0 in ...

A: Let the polar coordinates of given point are ( rcos(thita), rsin(thita)) as shown on board.By compar...

Q: x1 J: (x2+2x)2 dx= (x2+2x)3 C (x2 2x)3 C + 3 (x2+2x)3 +C 6 22-1C + -2 2x)1+C

A: Click to see the answer

Q: Use a Maclaurin series in this table to obtain the Maclaurin series for the given function x2 In(1 x...

A: We know the Maclaurin series for ln(1+x). From there we find Maclaurin series for ln(1+x^3) by repla...

Q: find the derivative of the question in the picture please show all work

A: Obtain the derivative of the function.

Q: Water drains from the conical tank at the rate of 5ftmin 14. 4 10 Exit rate: 5 ft/min a. What is the...

A: By using the concept that the sides of similar triangles are proportional, therefore, the ratio of r...

Q: The funciton f in the figure satisfies the lim f(x)=5 as x approaches 4. Determine the maximum valu...

A: (A) From the inequality |f(x)-5|<1 , we\'ll find range of f(x) first.

Q: Evaluate the following integrals (a) x^5dx (b)(5^2+x^10)dx (c) (12x^5+12x^3-7)dx (d) (x^3-7-(3/x^4))...

A: You have asked a question with multiple sub parts. I will address the first three of them. Please po...

Q: Use a reference triangle in an appropriate quadrant to find the given angle.

A: The given equation is,

Q: 3x2-3 and y(0) = 8, then y(1) = If dx 4. 12. 0. 8 6.

A: As a first step, let\'s rearrange the term. Please see the white board.