Verify Green's Theorem by evaluating both integrals for the given path. [x² αx + x² or = // (+1) ++) an C: boundary of the region lying between the graphs of y = x and y = x² √y² dx + x² dy= // (+/-^^^)o^ - [ ay

Q: Sheldon is being chased back-and-forth by a dog along Euclid Avenue. His directed distance (in…

A:

Q: √x² +16 dx

A:

Q: • [F. dr. Evaluate F(x, y) = xi + yj C: r(t) = (3t+1)i + tj, 0 st≤1

A:

Q: Show complete solution. Let S be the surface with equation y = (4x2/9) + z2 a. Write the equation…

A:

Q: Using trigonometric substitution to evaluate:, find dx * √x + √2-x² dx, O 3 cosø dø O 3sec^2 Ø dø O…

A:

Q: Each side of an equilateral triangle measures 3cm, with a possible error of 0.1cm. Using…

A: Given

Q: 1- Evaluate the following limits, if they exist. If they do not exist, state why.! lim f(x), where…

A: Given the query is to find the limit of the expression.

Q: Find the area of the region bounded by the given curves. Decide whether integrate with respect to x…

A: Given curves: y=ex, y=xex We have to find the intersection points of both curves Therefore, ex=xex…

Q: ∫((e3x)/(5+2e3x))dx

A:

Q: 4. (y² cos x - 3x²y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e

A: exact differential equation

Q: Evaluate the definite integral. NOTE: Enter the exact answer. So||ti + Bij||dat 1717- = 13 X

A:

Q: Consider the surface of equation z = x2 + y² . What is the equation for the tangent line to S at the…

A: We need to find equation of tangent line.

Q: ck < cre ISP Question af Calculate for the function f(x, y) = x² + y². dr Select the correct answer…

A:

Q: f(x) = 3x²+x+7. Approximate fo trapezoids. O a. 60 Ob. 44 Oc. 30 Od. 22 f(x)dx using the trapezoidal…

A:

Q: 3x a) fx5e³x dx 2x² + 3 c) f x(x − 1)² dx TU b) f sin³ xdx 4 d) f tan5x sec³x dx

A:

Q: Evaluate the definite integral. NOTE: Enter the exact answer. 10 S™ ||ti + 1²i|| dt

A:

Q: Quiz 2.1- Evaluating Definite Integral Evaluate the following and post your answers in the g.…

A:

Q: 2. Write the given (total) area as an integral. a. The area above the x - axis and below y = 4x²

A: Here , we have given a function  y=4-x^2 Which is an equation of parabola. Now we have to find out…

Q: log(is²t) + 1 log; 10 + logn C logn, 10

A:

Q: 2. Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 - x²…

A:

Q: Find a formula for the function f(x) such that f′(x)=tan⁡(x)x and f(5)=8. f(x)=  +∫   t= t=

A: This is a problem related to integration of the function. Derivative is given now by performing…

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A:

Q: 21. SHOW YOUR WORK Solve the system of equations in three variables: x - 3y + 2z == 10 2xy + 3z =- 9…

A:

Q: X √2x²-4x-7 dx

A:

Q: 2(-3x+1), dx

A: I=∫ 32(-3x+1) 2-3x dx21-3x =t21-3x ln2  ddx(1-3x) dx=dt-3 ln(2) 21-3x dx=dt2-3x dx=dt-6 ln 2

Q: x1/2 dx x3/4 + 1 Let x = z8 dx = 8z7dz Is the substitution the most appropriate one? Explain your…

A:

Q: Using trigonometric substitution to evaluate: The first thing we'll need to do here is complete the…

A: Here, we just need the complete square for the factor in the denominator (40-6z-z2)

Q: In x dx = fx²dx fln x dx = (Inx-1) + C the solution correct? If your answer is yes, provide the…

A: Given query is to find the solution of the integral.

Q: Use technology to find a local maximum and two local minima of the graph of the following function.…

A:

Q: ∫((cos3x)/(1-sinx))dx

A: We have to find the integration.

Q: Use a computer algebra system to graph f and to find f' and f". Use graphs of these derivatives to…

A: As per our guidelines, we can answer only three sub-parts in a single request. Kindly re-post the…

Q: Express the limit as a definite integral on the given interval. lim Σ Σ x;* -ΔΧ, [1,4] 0-700 (x;*)2…

A: To express the given limit as a definite integral.

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: Given

Q: 4- 3- 2- 1- X▶ 1 2 3 ZA 10 4 13 3 P 2 Ty 1

A: we have given 3D cartesian coordinate system

Q: 3. Find the area of the surface cut from the nose of the paraboloid x = 1-y²-z² by the yz-plane. Do…

A:

Q: Let f(x) = √√√x – 2. a) Find f(x + h): b) Find f(x + h) - f(x): c) Find_f(x+h)-f(x). h d) Find…

A: We have to solve multiple part

Q: Find all solutions to the equation. 2 cos x cos x=0

A:

Q: ∫sinx sin(cosx) dx

A: ∫sinxsincosxdxLet u=cosx=∫ -sinudu=-∫sinudu=--cosuSubstitute back u=cosx=--coscosx=coscosxAdd a…

Q: While measuring the side of a cube, the percentage error incurred was 3%. Using differentials,…

A:

Q: 2. Evaluate fy³ dx-r³ dy, where C is the circle of radius 2 centered at the origin, in the following…

A:

Q: Use the formula k(t) k(t) = ||r' (t) x r"(t)|| ||r' (t)||³ - r(t) = t²i+t³j to find k(t).

A:

Q: A plane flying horizontally at an altitude of 3.4 miles and at a speed of 790 mi/hr passes directly…

A:

Q: 7- Differentiate Y= f(g(x)) h³(√x)

A: Given that,     y=fgx4h3x

Q: Evaluate the integral of the following using Miscellaneous Substitution

A: We have to find the integral.

Q: A container that has 5 L of water with 1 kg salt dissolved is to be filled by pure water at a rate…

A:

Q: rocket is launched from the ground at an angle of 0.65 radians, and the rocket travels in a straight…

A: Given query is to find the height of the rocket.

Q: 9. (a) This is true. (b) This is false. 5 dx = 5x + C

A: topic - indefinite integral

Q: A hive of bees contains 27 bees when it is first discovered. After 3 days, there are 36 bees. It is…

A:

Q: Use synthetic division to find the quotient and the remainder. (3x4 -8x3+8x-5)÷(x-2) (3x4…

A:

Q: Solve the equations in Exercises 1-16 by the method of undetermined coefficients. y" 3y 10y = -3

A: