yV1)

Q: Calculate the directional derivative in the direction of v at the given point. fx, v)- tan Cy). -(1,...

A:  The partial derivatives of f(x,y) at the point (x,y)=(5,2)are:

Q: Find the derivative of y with respect to x.

A: Assume z=x^5+1. Then found derivative dy/dx using the chain rule.

Q: how to find  Find the exact length of the polar curve. r = θ2,    0 ≤ θ ≤ 7π/4

A:  The polar curve I given as, r = θ2,    0 ≤ θ ≤ 7π/4.The formula to calculate the exact length of th...

Q: Let H(x)=4f(x) + 5g(x), where the graphs of f and g are shown in the figure.  Find H`(1).

A: Firstly, we find the function y=f(x) , which is linear function , as  it is  a equation of straight ...

Q: Graph the following function.  Then use geometry to find the area and net area of the region describ...

A: Graphed the lines first. Area between y=3x-6,x axis and x=8 is above the x -axis (Blue shaded area)....

Q: differentiate f(t) = t^(1/3)/ (t-3) On the solution guide on the first step for the numerator, we ha...

A: Explanation:Consider the term t1/3.It is known that adding and subtracting a same number to any numb...

Q: Consider the function g(x) = |(x^2 - 4)/(x+3)| do the following: a) Give the domain of the function ...

A: a) First obtain the singularity for the given function as follows.The denominator of the given fract...

Q: I need help about solving this problem. a) How do I find the time required to reach the maximum amou...

A: Let F be the amount of fertilizer. In 1 minute 1 gallon of solution comes in and 5 gallons of soluti...

Q: Evaluate the integral.   Integral from nothing to nothing hyperbolic cotangent StartFraction x Over ...

A: Refer to the integral,Rewrite the hyperbolic cotangent as,

Q: Fourier's Law of heat transfer​ (or heat​ conduction) states that the heat flow vector F at a point ...

A: Given that,

Q: Help with #10

A: The acceleration of the moving particle is given by,a(t)=2ti+etj+cos(t)k       To find the velocity ...

Q: Given f(x) = x^3 + 3x - 2 , find y = (f ^-1 (x))' at the point (2,1)

A:

Q: using the formula attached to this question find the GINI Index if the Lorenz Function is Y= 0.92x1....

A: The given Lorenz function is,

Q: find the domain and range of f(x)=X5+x (the last x is supposed to be squared) and domain and range o...

A: Given information:The given function is f(x)=X5+x^2  and g(y)=1/y-2.

Q: Determine if y=e−x+8x−9 is a solution to the initial value problem given by y′+1=8x−y and y(0)=−8.

A: The given differential equation is y′+1=8x−y.The solution of the deferential equation is given as, y...

Q: dy If y 22 x, then dx 9.7 1. O 22 0. O 5. N O O O OO

A: The given equation is y=22+x.

Q: If y 3 , then dx 5x2-3 10r2 3V/5x2-34 35x2- 3) 5x2-3 10x 3 3(5x2-3)2 10r 3 35x2-3)

A: Find the derivative of the given function.

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: 150 100 50 20 40 60 3. Suppose that a population develops according to the logistic equation (c) Use...

A: Given that a population develops according to the logistic equation

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

A: Obtain the derivative of the 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: graph quadratic function f(x) = -3x2- 12x -1

A: Consider the given equation

Q: lim x→3(2x3 -12x2 +5x+3)

A: We have to evaluate the limit as shown on white board.Let’s call (2x3  - 12x2  + 5x + 3) as f(x)

Q: Find the point on the surface x2 − 2xy + y2 − x + y = 0 closest to the point (3, 4, −5).

A: Consider the provided surface

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

A: The given function is,

Q: calculate the integral of: e(x^2/2)

A: We'll use the Maclaurin series expansion for e^(x^2/2).

Q: Help with #4

A:

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: Let R be the region bounded by the following curves. Find the volume of the solid generated when R i...

A: The given curves are y=x, y=4x, y=16.The graph of the region formed by these curves is,

Q: The revenue from the sale of a product is, in dollars, R = 1500x + 3000(3x + 3)−1 − 1000 where x i...

A: The revenue from the sale of a product is, in dollars,R = 1500x + 3000(3x + 3)−1 − 1000where x is th...

Q: Which of the following limits could be evaluated using L'Hopital's Rule? Indicate all the apply. Sel...

A: (A) This limit was not in form 0/0 or infinity/infinity. So we can\'t apply L\'Hospital\'s rule for ...

Q: 2. (4.6) penicillin is sold at a price of $200 per unit. The production cost (in dollars) for x unit...

A: C(x) and P(x) shows the total production cost function and the profit function of penicillin.

Q: y′=−3x+9 Determine the particular solution to the differential equation that passes through the poin...

A: The given differential equation is y’ = –3x+9.

Q: Find the relative maxima, relative minima, and points of inflection and sketch the graph for the fun...

A: We have to find the relative maxima, relative minima, and points of inflection and sketch the graph ...

Q: Find the domain: g(x) = ln(e^x -5)

A: The domain of ln z is z>0. We'll use the same concept here. So e^x-5>0. 

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: 13. A 13 foot sliding ladder is leaning against a house when its base starts to slide away. By the t...

A: We are given diagram as

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

A: The given function is given by

Q: 3ln xy′−9x2 y′=4x4  What is the order of the differential equation shown above?

A: The given differential equation is ,3ln xy′−9x2 y′=4x4  The order of the differential equation is th...

Q: Let h(r) =log2 (x - 3) + 1. a. Find the domain of h(x). b. Find the a-intercept of the graph of h(x)...

A: Given function is: 

Q: PK P (K-P)e 8. Scientists use the Logistic Growth function P(t) = to model population growth where P...

A: The logistic growth function is given by,

Q: please explain how to solve this problem

A: Consider x be the number of times the price is reduced by $0.05.

Q: For each of the following integrals, indicate whether integration by substitution or integration by ...

A: Known fact:Integration by parts:When an integral contains the product of two functions, then integra...

Q: A fence is to enclose a lot with area 100 square meters. The front of the fence (considered the east...

A: Let the length of the east-west side is = x meter and the length of the north-south side is = y mete...

Q: Find the producers' surplus at a price level of p $51 for the price-supply equation below. S(x) 5+0....

A: Given price-supply equation is, 

Q: During the first 4 months of employment, the monthly sales S (in thousands of dollars) for a new sal...

A: During the first 4 months of employment, the monthly sales S (in thousands of dollars) for a new sal...

Q: find the volume aquired by taking by region bound by  y=x^2 and  y=x^4 and rotating it around x=-1

A: To calculate the volume bounded by the curve y=x2 and y=x4 which is rotating about the line x=-1. No...

Q: 2x4 +4x3 y″−6(lnx)y‴=−3x3 −2x5 y(4) +7(lnx)y′   What is the order of the differential equation shown...

A: The given differential equation is ,2x4 +4x3 y″−6(lnx)y‴=−3x3 −2x5 y(4) +7(lnx)y′. The order of the ...

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.

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...