Use the formula k(t) |r(t) × r"(t)|| x r" (t)|| to find «(t). ||r(t)||° r(t) = ti+ t5j «(t)

Q: (-x+82.762) 1(x) = 0.5e - 25.7 12 М m(x) — 0.15(х - 90)2 — 25.7

A: To find thee first and second derivative of the functions given.

Q: Find a value for k that will make the given function a probability density function. f(x) = kz, on -…

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Q: 7 dx x² + 52 Integrate: + C

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Q: 5. By Chain Rule , evaluate b. y' for y = u² + 2u and u = x² + 2 %3D

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Q: raluate the following definite integrals.

A: Topic:- definite integration

Q: /12. É (sin *xcosx+ sin xcos.x) dx

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Q: rrent Attempt in Progress Evaluate the line integral using Green's Theorem and check the answer by…

A: Greens theorem

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 5 cos(t)i + 11 sin(t)j +…

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Q: 4. Consider the figure below. y=4 x Find the volume of the solid generated when the shaded area a.…

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Q: Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee…

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Q: dx (х -1)3

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Q: Evaluate the line integral (8x + 7y)dx + (2x - 7y)dy along the curve C: a = 8 cos t, y = 16 sin t (0…

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Q: The derivative with respect to x of | (3Vi-1) dr is 3x – 1 by the 2nd fundamental theorem of…

A: Given that,         ∫3x3t-1dt

Q: Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding…

A: The solution is given below.

Q: (ar3+ bx2+ cx) dr =2b x2dx where a,b and c are constana A) True

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Q: + 3x² 4)dx

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

Q: V10x – 7y – 10 Find lim by rewriting the fraction first. 10x - 7y – 100 (x,y)→(10,0) 10x - 7y + 100

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Q: For the series below, (a) find the series' radius and interval of convergence. For what values of x…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin(In 12x) dx Cos In x +…

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Q: Evaluate the definite integral

A: Evaluate the definite integral .

Q: EXAMPLE 6 Evaluate the following integral. tan (r) dr SOLUTION First we write tangent in terms of…

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Q: Given / f(x)dx = -3 and / g(x)dx = 6 , evaluate (a) / ise) – 59(=)|dz 1 *(x) + (e) [ 15(4) – o(=) +…

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Q: If f(x) = [ V19+ t² dt , find f'(3)

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Q: Find V· (V × F) if F(x, y, z) = 4 sin ci + 7 cos(9x – 10y)j + 10zk. V · (V × F) =

A: Given F(x,y,z)=4sinx i+7cos(9x-10y) j+10z kTo find∇·(∇×F) first we need to find ∇×Fwe know that ∇×F…

Q: dy a. Use implicit differentiation to find dx b. Find the slope of the curve at the given point.…

A: Given query is to find the derivative and the slope of the curve.

Q: Solve the initial value problem y' = xe ; y(-1) = 3

A: We can solve the initial value problem as below.

Q: Solve the separable differential equation dy 0.7y, and find the particular solution satisfying the…

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Q: lim In(z – 1) – In(x“ – 1) = %3D

A: Given

Q: 2. A turns 100 RPM and B 150 RPM as shown; they are connected by rolling cones. Calculate the cone…

A: Solution: wa = 100 rpm wb = 150 rpm

Q: Problem 3.4 Parameterize the following surface. Then, integrate the given function over the…

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Q: Find the indefinite integral by using the substitution x = 8 tan(0). (Use C for the constant of…

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Q: If the profit function for a product is P(x) = 6400x + 80x² – x³ – 190,000 dollars, selling how many…

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Q: Find y': y = ar csc(2a2)

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Q: Find div F and curl F if F(x, y, z) = 13y'2*i – 11x°z®j – 7xy°k. %3D div F= 0 curl F=|(-35 z y³ + 99…

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Q: Find div F and curl F if F(x,y, z) = x2°i+ 4y°x²j+ 2z²yk. div F=|2° + 12 y? x² + 4 z y curl F= 2 z2…

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Q: The derivative with respect to x of (3i-1)ar is 3-1 by the 2nd fundamental theorem of Calculus A…

A: let f(x) =∫3x ( 3t-1) dt

Q: Find an equation of the tangent plane to R(u, v) = (e" sin u , e" cos u , e¯º ) at the point where u…

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Q: Improper Integral. KINDLY EVALUATE and Identufy whether convergent or divergent

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Q: / (3Vi-1)dt is 3 -1 by the 2nd fundamental theorem of Calculus. The derivative with respect to x of…

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Q: 2. C sin $ 2wcos° 2wcw 3. If f(x) = Vi19+r² dt , find f'(3).

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Q: Solve the seperable differential equation 10yy' = x. Use the following initial condition: y(10) = 7.…

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Q: 10 10 If f(x) dr = 17 and f(x) dr= 12, then f (x) dr =5 A True B False

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Q: Evaluate the integral directly by integration with respect to x and y. 4 x= (y/4)+ 1 4x - y -dxdy 4…

A: We have to find the value of the double integral ∫04∫x=y4x=y4+14x-y4dxdy Since dx present first in…

Q: Evaluate the integral below by interpreting y=f(x) it in terms of areas in the figure. A1 The areas…

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Q: (a) rªr- (b) y2 (c) e-4z+3e7z=3 ,71–3 (d) In(ez)

A: we have to simplify

Q: x2 + xy? lim (x,y)→(1,2) x4 + 2y2 or show that it does not exist. 2. (a) Evaluate the limit + xy? or…

A: We need to find limit.

Q: Use substitution to find the indefinite integral. Зх + 7 (6x + 28x) 5 3x +7 (6x² + 28x) =xp.

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Q: Kindly

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) COS X dx (sin x)20

A: Given, ∫cosxsinx20dx We have to evaluate the indefinite integral.

Q: Find the area of the region enclosed by the curves y=x2−2 and y=2.       Question content area…

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