Given the curve y = x' and the line y = 2 – x. Find the area of the region bounded by the curve and line.

Q: Find the volume of the solid that results when the shaded region is 6 revolved about the indicated…

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Q: Find the slope of the tangent line to the curve y = (1+4x)? at the point x = 2.

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Q: * ?Which of the following equations is an exact differential equation + 1) dx - xydy = 0 2xydx + (2+…

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Q: Solve the equation .11 y" + 3y' + 2y = x2

A: Given, y''+3y'+2y=x2 First let's find the Complementary function Re-writing the given equation as…

Q: How can we write out the summation of this notation

A: Topic:- simplification

Q: 12. Find an equation for the tangent plane to the surface given by 2xy = 2z2 - ryz at the point…

A: Use tangent plane formula

Q: Find the x- and y-intercepts for the function. x+1 r2+36 f (x) Enter your answers as points, (a, b).…

A: The given function is: fx or y=x+1x2+36   As we know that; To determine, x-intercept, we need to…

Q: Solve the equation .11 y" + 3y + 2y = x2

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Q: 11. ſ sin? x cos² x dx

A: Given ∫sin2x cos2x dxTo find integration:

Q: 3

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Q: 5. Evaluate the limit of (x^3-2x^2-x+2) /(x^2-4) as x approaches 2. a. a b. % с. 2/5 d. 4/7

A: Note: Since the student has posted multiple questions but first question (question number 4) is…

Q: There is a line through the origin that divides the region bounded by the parabola y = 4x – the…

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Q: Evaluate the indefinite integral. 8 + x*dx + C

A: topic- indefinite integral

Q: Find the limit.

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

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Q: An object is moving with velocity (in ft/sec) v(t) = t – 16. Find the displacement and total…

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Q: This problem has two parts. The second part will appear after you answer the first part correctly.…

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Q: There is a function                                                           f(x,y)=3√x3 + y.…

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Q: Use the Two-Path test to show that the following limit does not exist. (Use y=x2) lim (x,y)→(0,0)…

A: Using Two-Path test we will evaluate.

Q: Find the slope of the tangent line to the curve y = (1+ 4x)7 at the point x = 2. %3D

A: Slope of the tangent line is obtained by just derivative of the function  wrt the independent…

Q: 258. A spherical balloon is filled with air at the rate of 2 cu cm/min. Compute the time rate of…

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Q: This equation is an example for linear equations dy y = = x²e* dx True False O +

A: Any differential equation of nth order is linear if it is of 1st degree and donot have product of…

Q: If tan 0 = - n<0< , find the exact value of each of the following. 2 이 (a) sin (20) (b) cos (20) (c)…

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Q: Find the exponential function that contains the points (2,48) and (3,192).

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Q: Show that the following functions satisfy Laplace's equation dx? = 0. dy? f(x, y) = x³y – ry³

A: Given :f(x,y)=x3y-xy3

Q: Consider the equation a 4y" + by + cy = 0 the constants a.Gm are real and different from zero, the…

A: To find the inequality between b and c.

Q: V10 – Vx dx 3 2x2

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Q: 1 dx

A: This question can be solved using the concept of definite integral.

Q: Given the following functions: f(x) = cos(x) g(x) = x7 + 1 d d Find f(g(x)) and g(f(x)). (Use…

A: Given the following functions: fx=cosxgx=x17+1To find ddxfgx and ddxgfx.

Q: * This equation is an example for linear equations dy y = x²e* + dx False O True

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Q: Compute f(x)dx (6 points) f(x) = { 2x if x<1 4 if x21

A: In this we have to do the integral of given function so I'm providing hand written solution for this

Q: Use the Fundamental Theorem of Calculus to find the "area under the curve" of f(x) = 4x + 7 between…

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Q: Sketch the graph of an example of a function f that satisfies all of the given conditions. f(x) = 4,…

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Q: Find f, and f, as functions if 2y f(x. y) = y+ y + cos x

A: This question is related to differentiation, We will solve it using given information.

Q: Write an expression for the nth term of the geometric sequence. Then find the i a, = 8, r = n = 10…

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Q: lim Max Ax Ef xi Ax, , is equivalent to lim Efa+iAx)Ax with Ax = 5 _b-a 1. The Riemann sum, AX, n00…

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Q: 00 dz Either show that the improper integral converges and find its value, or show that it diverges…

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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

A: As we know that; The critical number of the function, y=gy can be determined by solve the equation…

Q: (V10 – Vx dx 3 3 V2x2

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Q: "Suppose w =+, x = cos² t, y = sin? t, z = dw Evaluate at t = 3, by using the Chain Rule dt

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Q: any solutions does the equation 2 + 6 (x 4) = 3x - 18 + 3x have?

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Q: Q1: Find dy/dx of the following functions: 1. x'e? y = log2 2Vx+1 2.

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: 8. Evaluate the limit of (4x^2-x)/ (2x^2+4) as x approaches a. a. 2 b. 4 с. а

A: We have to find limit.

Q: Find u + v, u - v, and 4u 5v. Then sketch each resultant vector. - u = (-4, 2), v = (3, -6) %3D (a)…

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Q: Q.4 Let Ø be a scalar point function defined as follows Ø = x3 + y3 + z - 3xyz. %3D 4.1 Find the…

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Q: In the notation for definite integral, | f(x)dæ, a

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Q: Se* sin e*dx

A: We have to find integrating of given Questions

Q: Using Sandwich Theorem 3n2 + 1 an = (-1)" n3 – 4 | O diverges O converges to 1 O converges to -1…

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Q: 2 tan(x)dx

A: This question is related to definite integration, we will solve it using given using given…

Q: by the suitable solution Full the following blanks (Undetermined Coefficients method) If y" +y = 2x…

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