Refer to the given below. Find the indefinite integral. Simplify your final answers (Just like how we simplify in our discussions). i. ji. iii. iv. V. 1 Attachment(s) - t. [(2r*+12 - 5)dx it. [(4x)(7x – 5)dx (-4V)a iv. (4secxtanx + csc?x)dx v. (sin?x+ cos²x)dx

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Q: 5. By Chain Rule , evaluate a. y' for y = u? + 4u and u = 4x3

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

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Q: Find y': y = arc sec(x²) y = xVx - 1 2 y : xVI -x 2 y = xVx -1 x Vx - 1

A: Given: y=arcsec(x2)y'=dydx=ddx(arcsec(x2))We know that ddx(arcsec(u(x)))=11-1(u(x))2…

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Q: 4. a = 20 m [W 30°S] b = 30 m [W 40°N]. Find a - b. %3D %3D

A: We need to find a-b.

Q: N h(x) = -0.8(x + 5)+39.9482 i(x) = 2-0.8(x-43.79)

A: 7) h(x)=-0.8(x+5)+39.9482 8)i(x)=2-0.8(x-43.79) 9) j(x)=0.1(x-57.5)2-0.0025(x-57.5).

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Q: X= 6 The area enclosed by the curves Y= and y= 2x from x= 1 to x= e is 2) e +1 O 3) +1 O 4) 2-2

A: Given query is to find the area enclosed by the curves.

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A: Here, the given surface is  6x2+y2-3z2=4⇒f(x,y,z)=6x2+y2-3z2-4 Let, P(x0,y0,z0) be the point of…

Q: Question 1 Which of the following is false? O yofe" = eu . Ine u (x) In e O yof log, u = u' (x) In a…

A: We can solve as follows

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Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 5 cos(t)i…

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Q: Evaluate the following definite integrals. 3. If f(x) = V19+f dt ,find f'(3).

A: We can solve as follows

Q: Verify the Divergence Theorem by evaluating F.N dS as a surface integral and as a triple integral.…

A: Here, using the Divergence Theorem, ∯F·Nds=∫∫∫v∇·Fdv Here, F=xy,z,x+y So, ∇·F=∂F∂x,∂F∂y,∂F∂z=y,0,0

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A: To find the average value of the function,      fA=1b-a∫abf(x)dxWe have, f(x)=500-90x, a=0, b=2

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Q: Current Attempt in Progress Use Green's Theorem to evaluate the integral. Assume that the curve Cis…

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Q: 21 Given 3x7 +8x5 - , determine, y" O 630x4 + 480x² + 126 5x4 O 840x3 + 360x 504 - 504 O 2520x3 +…

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A: We know Implicit differentiation of ax+by=c is given by, a+bdydx=0 ddx(xn)=nxn-1 , for any real…

Q: Given a function f(x, y) = e"y². (a) Find the gradient of f. (b) Evaluate the gradient at the point…

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Q: Find the points on the surface 6x² + y² – 3z² = 4 where the tangent plane to the surface is parallel…

A: We need to find points of intersection.

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

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Q: Question 4 Determine the derivative of the given function: y = (e + e*)3 Oy = 3(e+e) (e" - e) Oy =…

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A: answer is in next step

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.

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Q: sin 201/1+ 2 sin 0/cos? 0 (sec² 0 – 1) d0 1. |

A: To find the following antiderivative.∫sin 2θ1+2 sin θcos2 θ sec2 θ-1 dθ

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A: Area bounded by curves :   If f(x) and g(x) are two continuous function on a,b and f(x)≥g(x) on a,b…

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Q: 3. If f(x) = [ v19 +r² dt , find f'(3).

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A: Given problem:- Find the conservative vector field for the potential function by finding its…

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Q: 1. Find the area bounded by the parabola y=4ax, the x-axis, and the lines x=4a, x=9a.

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Q: dy Given the equation below, find dæ - 51a" + 7a"y + y10 = - 43 dy 172 (15 – 1422y) 29. dæ Now, find…

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Q: 10 8. 10 If f (x) dr= 17 and/ f(x) dx= 12, then f(x) dr=5 A) True Ealce

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Q: Find div F and curl F if F(x, y, z) = 4y³z'i – 11a"z°j – 4xy°k. - -

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Q: Find dy/dx. x = Vt y = 9-t dy dx

A: Here, x=t3y=9-t