Find r'(t) r(t) = 6yEi + t²/ij + In[? }« %3D r'(t) = %3D

Q: 4. a) Find the average value of the function over the given interval. f(x) [4, 25] Vx'

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Q: H.W (5) Solve the following differential equations of (3x -6xy)dx+(-3x' -2y)dy 0

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Q: Verify Green's Theorem by evaluating both integrals aN dx + x² dy = / / dA ay y2 ax for the given…

A: To verify green's theorem by evaluating both the integrals.

Q: Referring to Figure 11, suppose that F. ds = 37, F. ds = 77 Use Green's Theorem to determine the…

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 4yHx²j +42?yk. 5: 112. div F= curl F=

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Q: Describe the graph of the equation. r = 4 cos t i – 14 sin t j + k O An ellipse in the plane z = 1,…

A: Here, the given parametric equation is: r=4 cos t i-14 sin t j+k⇒r(x(t),y(t),z(t))=(4cos t, -14 sin…

Q: Use a change of variables (Substitution Method) to evaluate the following definite integral. Show…

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Q: Describe the graph of the equation. r= 5 cos t i - 18 sin 1 j +k O An ellipse in the planex = 1,…

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Q: Derive the Maclaurin series expansion for f(x) = COS x

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Q: AX = B is a matrixial representation of a lineal system of equations. Over the augmented matrix (…

A: Here we have to choose the correct option.

Q: im Y cosx tZx 7x¢ with squeze thearem

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Q: Calculate x sin(y)dxdy

A: On solving this we will get

Q: Inx 6. lim,

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Q: If x + 1 f(x) then find the global maximum of on the interval [1, c0) Write DNE if there is no…

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Q: Find the constants a and b such that the function is continuous on the entire real line. x 5

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Q: 3. Use the Fundamental Theorem of Calculus to evaluate the definite integral 16 x Vx dx 4

A: Given: ∫416xxdx Simplifing the given integral∫416xxdx=∫416x(x12)dx                 =∫416x1+12dx…

Q: dy If y = tan? x, find da

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Q: Tabular representations for the functions f, g, and h are given below. Write g(x) and h(x) as…

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s)…

A: topic - differential equation

Q: (a) Alina needs to make a flyer for her band's concert. The flyer must contain 20 square inches of…

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

Q: he curvature and the radius of curvature at the stated point. r(t) = 3 cos(t)i + 4 sin(t)j + tk; t 2…

A: Please refer to the image below

Q: Find the interval of convergence for the Maclaurin series expansion for f(x) = e".

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Q: CoS X F 2x 7x

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Q: Find the volume of the solid generated by revolving the region R bounded by the graphs of the given…

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Q: Find the derivative of this function

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Q: Calculate the area of the region bounded by the graphs of the given equations. x 2y2- 4, x = y2 + 5…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

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Q: tan(0)² cos(0) d0

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Q: Compute each sum below. If applicable, write your answer as a fraction. 4 + ...+ 4(3)- 0 + 4(3) +…

A: Use geometric series sum concept

Q: ||r'(t) x r"(t)|| Use the formula k(t) to find k(t). 13 r(t) = t’i+t5j K(t) =

A: We have to find k(t)

Q: Find an equation of the hyperbola having foci at (3, -11) and (3, 7) and vertices at (3, -4) and (3,…

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Q: 1 — х b. lim х36 (х — 6)2

A: b) limx-6(1-x) /(x-6) 2 a) limx-5 (x-1 sqrt(3x+1))/(x-5).

Q: Evaluate lim (x)/

A: We can find the  limit as below.

Q: (-1)"2"x" n=1

A: We will use ratio test to find radius of convergence.

Q: 20. Evaluate dædy by changing the limits of integration appropriately. e y/2

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Q: 2. Sheldon is being chased back-and-forth by a dog along Euclid Avenue. His directed distance (in…

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Q: Find the area inside the circle r = = cos 0, but outside the circle r = 1/2. Sketch the graphs first

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Q: x'y'y'+ xy' = 1 dy x' + y' dx 2ху dy 2 rv + 3v2

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Q: A swimming pool is circular with a diameter of 40 feet. Depth is constant along east-west lines and…

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Q: 9. A triangle has two sides represented by vectors OA = (2,-3) and OB = (3,1). Determine the…

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Q: find SCE) at timet V=-5t+5, S0) = 14

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Q: Consider the matrixes 0 3 -9 k A = O .B = ( , 7 7 62 k is a real constant M = (A-B-1)-1 If m22 = 14…

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Q: Solve for x. log x = - 4 0.0001 -0.0001 1.386 -4

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Q: у" — у' — бу %3D2, у (0) %3D 0, y'(0) = 0

A: Given can be written as (D2-D-6)y=2 The general solution will be y=CF+PI Complementary Factor(CF):…

Q: 2. Compute Ja F · ds for F c(t) = (t , In(1+ t²), e*) for 0 <t < 1 VV, where V(r, y, z) = 4x² In(1+…

A: Find your answer below

Q: Evaluate the given integral by changing to polar coordinates.     sin(x2 + y2) dA   R, where R is…

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Q: 2 _9 ii)lim- t-3 t2+4

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

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t-0. Q…

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Q: Find the volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y= 0, y = 7+a*…

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Q: x+x-6 lim X-2 x-2

A: Since you have asked multiple question, we will solve the first question for you as per our guide…