Equations are given whose graphs enclose a region. Find the area of the region. (Give an exact answer. Do not round.) h(x) = x2;  k(x) = the square root of x

Q: Solve the initial value problem below. 4y(8) + 6y" = 0, y(0) = – 1, y'(0) = 0, y"(0) = 1 y(x) =

A: we have to solve the given initial value problem: 4y3+6y''=0, y(0)=-1, y'(0)=0, y''(0)=1. we have to...

Q: Find the directional derivative of f(x, y, z) = xy²z³ at P(3, 1, 1) in the direction of Q(0, -5, 7)....

A: The directional derivative is  of scalar f  at point P  in the direction of  unit vector e¯ is     e...

Q: Give an example of each or state that the request is impossible.For any that are impossible, give a ...

A: (a) Consider the sequence xn=-1n . Here the occurrence of 1 is infinite times and it does not conver...

Q: Use the quotient rule to simplify the expressions.Assume that x > 0. √150x4/√3x

A: If a and b are non-negative , the square root of the product of ab is equal to the product of the sq...

Q: Help me fast......I will give Upvote.....

A: Consider the following points: Px,y=20,650Q1x1,y1=7.3,145Q2x2,y2=11,260Q3x3,y3=18.1,554Q4x4,y4=18.8,...

Q: erify all test hyp

A: Series:

Q: Solve the equation. Check the answer.x^((4)/(3)) = 81x=_____ (Simplify the answer. Use positive expo...

A: To solve for x,  x^((4)/(3)) = 81

Q: Find the absolute extrema of the function on the closed interval.   g(t) = t^2/t^2+5   {-2,-2}   Min...

A: I think the closed interval is [-2, 2] instead of [-2, -2] Substitute t=-2 in the given equation g(-...

Q: (d6/dx6)(x2 sin x)

A: Given function is fx=x2sinx    

Q: Use Descartes’s Rule of Signs to determine the possible number of positive and negative real zeros f...

A: Given function is fx=-2x3+x2-x+7 We have to find the possible number of positive and negative real z...

Q: A swimming pool is circular with a 40-ft diameter. The depth is constant along east-west lines and i...

A: Given: A given swimming pool is circular with a 40 diameter and radius 20. since height varies from ...

Q: Help me

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any ...

Q: Verify the identity sin 4t = 4 sin t cos3 t - 4 sin3 t cos t.

A: We have to verify the identity: sin4t=4sintcos3t-4sin3tcost We know following trigonometric identity...

Q: Find polar coordinates of the point whose rectangular coordinates are (0, -4). Express u in radians.

A: Given: x,y≡0,-4 we know that polar coordinate for given rectangular coordinatex,y is given by r,θ wh...

Q: The radius r and height h of a right circular cone arerelated to the cone’s volume V by the equation...

A: We have given thatthe radius r and height h of a right circular cone are related to the cone’s volum...

Q: Evaluate the following integrals.∫(y2/(y+1)4)dy

A:

Q: Show incomplete graph of the polynomial function f(x) = 2x4 + 2x3 - 22x2 - 18x + 36a. Find all the z...

A: Given: f(x) = 2x4 + 2x3 - 22x2 - 18x + 36

Q: Find the unique solution of the second-order initial value problem. y" + y' - 6y = 0, y(0) = 5, y'(0...

A: y''+y'-6y=0(D2+D-6)y=0D2+D-6=0D2+3D-2D-6=0D(D+3)-2(D+3)=0(D-2)(D+3)=0hence the roots areD=2,-3

Q: COMPOUND INTEREST In Exercises 23 and 24, determine the principal P that must be invested at rate r ...

A: Since you have posted multiple questions, as per our policy we will answer first question. Please re...

Q: Find the constant of proportionality k.y=(k)/(x), and y = 3 when x = 4.k = ______ (Type an integer o...

A:

Q: End behavior of an algebraic function Use limits at infinity to deter- 10x3 3x2 + 8 mine the end beh...

A: The function is given by f(x)=10x3-3x2+825x6+x4+2

Q: The measurement of the edge of a cube is measured to be 9 inches, with a possible error of 0.03 inch...

A: Given: The measurement of the edge of a cube is measured to be 9 inches, with a possible error of 0....

Q: Write a double integral that represents the surface area of z = f (x, y) that lies above the region ...

A: Given function Fx,y=2y+x2 Formula used: Surface area = S=∫R∫1+fx2x,y+fy2x,y  dA The region R: triang...

Q: Trigonometric integrals Evaluate the following integrals. ∫(csc2 x + csc4 x) dx

A: We know that, cosec2x=1+cot2x We have, I=∫cosec2x+cosec4xdx On solving further, we get our result as...

Q: (a) Find the derivative of f(x)=(x2+9)(8x−7) by first expanding the polynomials. f(x)= f'(x)= (b) Fi...

A:

Q: If x =1/k ln y, then y = ekx.Determine whether the statement is true or false. If the statement is f...

A: Given:x=1k lnyTo prove: y=ekx is true or false

Q: if none of the choices represents a correct answer, select the option “Other” and write your own ans...

A:

Q: What two positive real numbers whose product is 63 have the smallest possible sum? Let S be the sum ...

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Q: What is a dependent variable?

A: To explain what is a dependent variable

Q: Find dy if y = In* +1 7 -t dy dt

A:

Q: Differentiate implicitly to find the first partial derivatives of z. x2 + xy + y2 + yz + z2 = 0

A:

Q: Students in a psychology class took a final examination. As part of an experiment to see how much of...

A: Given that, Students in a psychology class took a final examination. As part of an experiment to see...

Q: Evaluate the following limit (write answer as a whole number): lim (sin x)tan x x->0+

A: Evaluate the following limit (write the answer as a whole number): lim (sin x)tan x x->0+  

Q: 38. Determine how many zeros are at the end of the numeralsfor the following numbers in base ten.a. ...

A: (a) The number given is 10! To find the number of zeros at the end of n!  Divide n by 10 and then de...

Q: The graph of g  is given.(a) Why is  g one-to-one?(b) Estimate the value of g-1(2) .(c) Estimate the...

A: Concept: The calculus helps in understanding the changes between values that are related by a functi...

Q: Find a formula for a function that has vertical asymptotes x = 6 and x = 8and horizontal asymptote y...

A: Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a ration...

Q: solve the inequality algebraicly and specify your answer in interval notation. 3/x-5 > 7/6x-4

A: Given: 3x-5>76x-4

Q: Question is attached.

A:

Q: find the volumes of the solids generated byrevolving the regions about the given axes. If you think ...

A: The volume of the solid is given by,              Volume=∫ab2π(radius)(height)dx Here, the radius wa...

Q: find a parametrization of the surface. (There aremany correct ways to do these, so your answers may ...

A: To find the parametrization of the surface. Consider the given equation of  the portion of the cylin...

Q: Use the definition of the definite integral to evaluate fo (2x – 1)dx. Use a right-endpoint approxim...

A: To Find: a. Use the definition of definite integral to find ∫032x-1dx.b. Use right-endpoint approxim...

Q: Evaluate the following limit. Use l’Hôpital’s Rule when it is convenient and applicable.

A: L'Hopital's Rule: If limx→af(x)g(x)=00 Then using L'Hopital's Rule, limx→af(x)g(x)=limx→af'(x)g'(x)

Q: Find the positive values of p for which the series converges. (Enter your answer using interval nota...

A:   Let  f(x)=1xln xp f is positive, continuous and decreasing so we can apply the integral test.  By ...

Q: Suppose f- is the inverse function of a differentiable function fand let  G(x)  = 1/f-1(x). If f(3) ...

A: Let us assume the g is the inverse of function f. Now, f(x)=g-1(x)g{f(x)}=x Differentiate the above ...