4 Sec

Q: Compute the directional derivative of g(x,y)=sin(pi(5x-5y)) at point P(1,-3) in the direction (15/17...

A: Firstly, we calculate unit vector in direction of vector u.

Q: For the following function f, find the antiderivative F that satisfies the given condition.   F(v) =

A: First, we find the general solution using integration. 

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

A: The function is given by,

Q: Is y=ex +8x+5 a solution to the initial value problem shown below? y′−y=−8x+3 y(0)=6 Select the ...

A: The given differential equation is y’-y=-8x+3.The solution of the deferential equation is given as, ...

Q: Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the ...

A: The given curve is y = x^2/3, x=1 and y=0. 

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: Please help me with this differential equation and identify P(x), Q(x) and v(x).

A: The general form of first order  linear differential equation is shown on board

Q: Help please..

A: We first calculate the value of cos x at x=0.5 

Q: Find the derivative of y with respect to x

A: we are given an inverse function 

Q: The equation abs(y/a)^n + abs(x/a)^n = 1, where n and a are positive real numbers.  Make a complete ...

A: The equation abs(y/a)^n + abs(x/a)^n = 1,

Q: 1. Indefinite and definite integrals including trigonometric functions and ones that will require th...

A: a. Integrate the given indefinite integral with respect to x as follows.

Q: Find the area, in square units, bounded by f(x)=3x+5 and g(x)=2x+1 over the interval [0,12]. Do not ...

A: Area of region between f(x) and g(x) over the interval [0,12] is computed as follows.

Q: What is the order of the following differential equation? −4x4 y=−5ln xy

A: Given differential equation is, 

Q: 8xy′+4(ln x)y)(4) +5x3 y′=−6x4 y−9xy″   What is the order of the differential equation shown above?

A: The given differential equation is,  8xy′ +4(lnx)y4 +5x3y′ = -6x4y - 9xy″.The order of the highest d...

Q: A circle has an initial radius of 50 ft. when the radius begins decreasing at the rate of 3 ft/min. ...

A: Area of a circle is given byDifferentiating the function of area with respect to time:

Q: Use the Divergence Theorem to compute the net outward flux of the vector field F=<x2 , -y2, z2&gt...

A: The vector field is given as

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

A: Given infromation:The given funcion is  

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: Determine if y=e2x −x+1 is a solution to y′−2x=−3+2y.

A: The given differential equation is  y′−2x=−3+2y.The solution of the deferential equation is given as...

Q: 5 dx In 26 In 24 '을 In 24 글 In 26 none of the above

A: Obtain the value of the integral as follows.

Q: What is the position at time t of a car that is accelerating at a rate of 5 meters per second square...

A: To determine the position of the car from the given data. (note that s =20 when t=2, not as given)

Q: A function and its first and second derivatives are given. Use these to find the relative maxima, re...

A: In this question, we have function, its first derivative and second derivative using that we have to...

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:

Q: A particle travels clockwise on a circular path of diameter​ R, monitored by a sensor on the circle ...

A: Before we get into the question, please recall the theorem that: An angle in a semi circle is always...

Q: Please help. Find the values of x for which the given geometric series converges. Also, find the sum...

A: (a)Consider the given geometric series:

Q: Kindly help

A: Refer to the question, we have to calculate the Taylor series for the provided function,

Q: The consumer price index (CPI) measures how prices have changed for consumers. With 1995 as a refere...

A: Given:The rate of change of CPI in dollars per year is dC/dt= 0.009t2 − 0.096t + 4.85, where t repre...

Q: Find the average value of the function f(x) = e-4x on the interval [0, 1/2].   please show and expla...

A: The function is given by,

Q: If p 8m2-9m + 3, then the rate of change of p with respect to m when m 1 is 16. 1 -9, 7. 2.

A: Approach:A clear relationship between "p" and "m" is given"p" is dependent variable while "m" is the...

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: How do you find the limit of f(x) of the attached equation?

A: Notice that the graph is discontinuous at x=3. 

Q: Find the area, in square units, bounded above by f(x)=6x2 −2x−19 and below by g(x)=7x2 +12x+21.

A: f(x)=6x2 −2x−19 and g(x) = 7x2 +12x+21.As a first step, we need to find the point of intersection of...

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

A: Calculation:The given function is f(x) = 2(5x)x defined on interval [0.05, 1].In order to find the l...

Q: if logx y = z, which variable(s) must always be positive

A: logxy = zWith respect to logarithm:The base of a logarithm should always be positive and not equal t...

Q: Find the equation of the tangent to (x2+/ 5x2-Уг at the point (1,1). 8.

A: Given curve is: (x2 + y2)2 = 5x2 – y2and the given point is (x1, y1) = (1, 1)Equation of tangent wil...

Q: 2 sec x Ay and the 2 In the figure to the right, the equation of the solid curve is y equation of th...

A: The curves are given by,

Q: Calculate the area, in square units, bounded by g(x)=4x+8 and f(x)=x2 +19x+62 over the interval [−9,...

A: We have to find area between f(x) and g(x) for given boundaries.f(x) and g(x) is given below:Graph  ...

Q: Approximate the area of the shaded region using the Trapezoidal Rule and Simpson's Rule with n = 4. ...

A: Given information:The value of n is 4. 

Q: If the formula describing the distance s(in feet) an object travels as a function of time(in seconds...

A: The distance s(in feet) an object travels as a function is s = 100 + 160 t -16t2.It is known that, t...

Q: Differentiate y = (s - sqrt(s) ) / s^2   I don't understand what happens on step 3 of the screenshot...

A: Here use quotient rule of differentiation which is,

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: Find the derivative of the inverse function  f(x) = x/x+2

A:

Q: Which of the following is the power series representation for f(x)? O A. B. 1 4k X Σ 4k k 0 1-x k 0 ...

A: Consider the power series representation for f(x4):

Q: lim x→-4   x2-16/x+4

A: The given function is f(x)=  (x2-16)/(x+4)The limit of the function is to be calculated

Q: (3x2+5)8x-92 fy(1x4 + x2 logarithmic differentiation gives y (32+5)(8r-92 1x44+x2 16 2x 3x2+5 6-x9 6...

A: We have to find derivative using lograthmic differentiation .Question is given below:

Q: If y x4x+3, then 2ix+3ix3 2i 3ix3 O (4x+1)/4x+3 2Ax+3 2x vi3Ar3

A: The function is given by,

Q: Do the domain of the following function:

A: Consider the provided function.

Q: The number of miligrams x of a medication in the bloodstream t hours after a dose is taken can be mo...

A: we are given a function  

Q: a), b) and c) please. I also forgot how to write interval notation....

A: To find the direction we have to graph the function v(t)= 3t^2-36t+105 ; [0,8]. And then we check th...

Q: Calculate the area, in square units, bounded by g(x)=4x−2 and f(x)=5x−15 over the interval [−11,4]. ...

A: Area of region between g(x) and f(x) over the interval [–11,4] is computed as follows.