Find the average value of f(x,y) - 5 - x - y over the rectangle R = {(x,y) 0≤x≤1, Osys2} 10 08 07

Q: Find the curvature of r(t) = (3t², In(t), t In(t)) at the point (3, 0, 0). K =

A:

Q: Calculate all four second-order partial derivatives of f(x, y) = 4x²y + 8xy³. fxx (x, y) = fay (x,…

A:

Q: Evaluate the definite integral. [° ( Z - ²3/) dx J₁ X

A: ∫16x6-9xdx

Q: Find the following for p =, q =, and r =. Find -2p - r

A: Given that,    p = -7, -6  q= -1, -11, r= 0,9 we have to find the value of -2p-r.

Q: 7) Find the area bounded by the line y = x and the parabola x = y² - 2y.

A: We know that the area formula int_a^b {f(y)-g(y)} dy

Q: Find the average value fave of the function f on the given interval. sec²(2), [0,7] 2 fave = f(0) =…

A: The given function is: fθ=17 sec2θ2 ;             0, π2

Q: a) lim (-2x¹) = 8118 ) lim (-2x¹) = xx ) lim -√x = 118

A:

Q: Construct a limit evaluation problem with an answer of 1.

A:

Q: 79. Give an example of a divergent sequence {a,} such that lim |an| converges. n→∞

A: To find a divergent sequence whose absolute sequence converges

Q: Evaluate the integral. (Use C for the constant of integration.) [In(√x) dx

A: Short Explanation::-

Q: You know that: ■ +5√3 food f(t) dt = 31 • ƒ(7) - 22 Evaluate: = I · ƒ(7) = 25 ľ 70 cos(x) f(10…

A: Let u=10 sin x Differentiation du=10 cos x dx

Q: Use interval notation to indicate the domain of x + 1 f(x) x² + 10x + 25 = Answer: * E Note: Input…

A: The given function is fx=x+1x2+10x+25

Q: 7) Refer to the information in Problem 6. Find the object's total distance traveled on the interval…

A:

Q: ly the Ratio Test to determine convergence or divergence, or state that the lim n→∞ an+1 an n n² + 1…

A:

Q: Divide the complex numbers below and leave the result in trigonometric 7(cos 150° +i sin 150°) 9(cos…

A:

Q: Find the four second-order partial derivatives. f(x,y) = 3x³y - 5xy + 8y fxx (x,y)= 216x y y (X,Y)=…

A: To find the four second-order partial derivatives. fx, y=3x9y-5xy+8y

Q: 3) Find the equation of the osculating plane of the helix x = sin 3t, y = 2t, at the point (-1, π,…

A: x=sin3t y=2t z=cos3t Point÷ -1,π,0 π=2t means t=π2

Q: 5. Integrate (a) [² 3x +7 dx + (b) fe' de (c) [5-13dt (Note your answer should have z in it. )

A: The Sum Rule: ∫fx±gxdx=∫fxdx±∫gxdx The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: A particle is moving with the given data. Find the position of the particle, s(t). a(t) = 2t + 5,…

A: a(t)=2t+5, s(0)=4, v(0)=-5 Find s(t).

Q: (c) Now estimate the area under the graph of f using eight approximating rectangles and taking the…

A:

Q: Practice similar Help me with this First, note that we know how to integrate 7 dx = 1=²+4² 1² da 2 x…

A:

Q: A man launches his boat from point A on a bank of a straight river, 2 km wide, and wants to reach…

A:

Q: 1. Find the general anti-derivative of each of the following functions. (a) f(x) = 3x² - 4x + π (b)…

A: General antiderivative of f(x) is given by F(x)+c , where c is constant and F'(x)= f(x) Simply we…

Q: 4) Suppose the velocity of an object is v(t) = 9t-t³, where v(t) is measured in feet per minute.…

A:

Q: Find the total mass of a 1 meter rod whose linear density 17 function is p(x) kg/m for 0 ≤ x ≤ 1 (x…

A:

Q: 1) An object moves from a point of origin 5 meters to the left. Describe the object's displacement…

A: An object moves from a point of origin 5 meters to the left. Describe the object's displacement and…

Q: are there any holes for this function,verticial or horizontal asymptotes?

A:

Q: 3) Find the area bounded by the parabola x = 9-(y-2)² and the y-axis.

A: We know that area formula int_a^b f(x) dx

Q: Write the vector shown on the graph below as a linear combination of standard uni vectors i and j.

A: Graph

Q: Evaluate the integral. 2x cos(9x) dx

A:

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A:

Q: 20. Practice similar Help me with this. Use the limit comparison test to determine whether For n ≥…

A: We have to to Check the convergence of given series.

Q: Use the graph of the rational function f(x) to complete the statement. As x 27, f(x)→ -10 OO -2 +∞ 0…

A:

Q: Use part one of the fundamental theorem of calculus to find the derivative of the function. g(x) =…

A:

Q: III. If f\x, y = x² cosy - y. e²y, then find all the second order partial derivatives.

A:

Q: L (4 + √36-x²) dx

A: Evaluate the definite integral  We know that the formula int_a^b f(x) dx=int_b^a f(x) dx

Q: 3. Practice similar Help me with this Find the quotient and remainder using long division for The…

A:

Q: 1. A rocket is fired at an angle of 25° to the ground and with an initial velocity of 120 m/s.…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) [7. 7z³e² dz

A: ∫7z3ezdz

Q: 4) IF F(2) = 20 and F'(x) 24 for all valves OF X, how small can F(5) Possibly be? Use mean value…

A:

Q: 1. Which of the following is not a D.E.? A. y"- 3y'=0 B. y dz = w(z)=0 I C. y A sinx + Bcosx D. L…

A: **As per our guidelines, we are supposed to answer only one question at a time. Since you have…

Q: 4) A region is bounded by the line x = -1, the line y = 2, and the curve y = 2*. Find the area of…

A:

Q: Use the standard Maclaurin series for sin(x) to find the first three non- zero terms in the…

A:

Q: 61. an = nsin RIS n

A: We find the limit of given sequence.

Q: The power series representation of 1 3x + 2 is: f(x) =

A: we need to find the power series representation of the function f(x)=13x+2

Q: 1.) d³s dt3 2.) x 3.) ди ду d²v dr² + U = EQUATION S 3 1 + (- 2² z əx² dv + t dr 13 ds dt 4 - st = 0…

A: Since you are asking multiple questions. We are answering only first three questions as per our…

Q: 1 (a - b) In (a − x) (b - x) X *)] = [K₂ t]

A:

Q: (iii) y = (3 + 2x)−5

A:

Q: The series Σ n=1 convergent. (-1) " n 0.9 Select one: O True O False Give your reasons is absolutely

A:

Q: 4 -2 -2 -4 h(x). 10 X

A: