Practice by Evaluating 1 VI-x² cos(a² + y³)dydx 0.

Q: ду Let y = In Vx² + 2z3 + cos(b³), find

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Q: What is y' of y = sin¹ (cos x)? O A. y' = ATHE sin + 1-cos² 1 O B. y' = 1 OC. y'= sin z 1-cos² z OD.…

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Q: Given y= 5e3X + sin x, -is dx A) 5e3x + cosx B 5e3x – cosx 15e3x + cosx D 15е3х — сosx

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Q: -3 Evaluate: ²¹²² ²³ y cos(z³) dx dy dz

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Q: Given: [ Scos(cos2x) sin2x dx Find: du O 2cos2x dx O -2sin2x dx -2cos2x dx O 2sin2x dx O O

A: ∫coscos2xsin2xdxLet u=cos2x.So,     du=-2 sin(2x) dx

Q: Compute -i + cos -i sin a - sin a + i cos a where a E (T, ).

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Q: dy Find if cos(xy) = x2 + y?. Show your work. dx

A: Differentiate wrt x

Q: Given that y = sin (t) and x cos²(4t*), hence find dx dy

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Q: Evaluate: Sv*+sin/x dx. A x+2cos/x+ C 2x+ cosx B + C 2

A: We have to solve the integral

Q: Evaluate cos zV1+ cos². dædy

A: Given double integral is                    T=∫01∫arcsinyπ2 cosx1+cos2x dxdy ⋯⋯⋯⋯⋯⋯ (1)

Q: Given dy find 36 Cos 6x y' dx sin 6x + c 6 sin 6x + c O-6 sin 6x O-36 sin 6x

A: here option a is true.

Q: the area outside r = 1 and inside r = 2 cos 0 is

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Q: Find 17. d Ssin (4x) cos(4x) dx

A: Use substitution to solve

Q: Se Ce cos (sin '(x)) COs (sin

A: We need to find the antiderivative of ∫ecossin-1xdv

Q: The coefficient of sin(x) in the antiderivative of Flx)=(cos() is 15/32 (use fraction form not…

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Q: 1 For cos2(xy) = , evaluate y' when x = 1.

A: The given equation is cos2xy=14. Calculate the first differentiation y' of the given equation at…

Q: Eliminate parameters A and B but not parameter C by differentiating x with respect to t. x=A cos…

A: x=AcosCt+B Differentiating wrt t, we get  x'=-ACsinCt+B Again differentiating, we get…

Q: // Show that y" + y = 0, given that y = 2 sin x + 3 cosx

A: First find the first and second derivative of the given function then simply put and simplyfy

Q: Use the substitution formula to evaluate the integral. (1 + cos 3t) 2 sin 5t dt 15 15

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Q: Show that y" + y = 0, given that y = 2 sin x + 3 cosx

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Q: B Integrate the following. * cos x' dx 2 a.

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: dy iven that x = e" cos 3t, y=e" sin3t, show that tan 3t + dx %3D 4

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Q: Ly = Ce* + C2 cos x + C3 sinx

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Q: Find Cuurtce at Pla,l, 이) (x 2y-1 Xe' î + X Cos (22), 3. (2²+)

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Q: The substitution u = tan |converts the integral 2 π/3 1 dx to: n/2 2 +sin x - coS X

A: Given,∫π22π312+sinx-cosx

Q: @ / Find if dy O J= \ntanh (+2 の= Cos (Cosスー) O3=109,(e CSCX +Sinx)

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Evaluate the equation below rsin 0 r3 cos 0 dr d0 0.

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Q: a2z a2z dz Q3) A: If e-(sinx + cosy), show that ax2 ду? at

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Q: H.w Evaluate;- Cos TT lt-1)idt

A: To evaluate:  1) ∫-∞∞δt-2e-tcosπt-1dt2) ∫03∫-∞∞t2+4δt-τdτ dt

Q: Let I = 3x*cos (x) dx. The approximation of / using the two- formula is:

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Q: (b) Find, where y= cos ecx- dx -4x+7

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Q: Q1 Evaluate 1, where: -So I = -3x cos 2x dx

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Q: Determine the concavity of y = 3 + sin x on [0, 2π]

A: The function y=3+sinx on the interval 0,2π. We have to determine the concavity of this function.

Q: ) // Show that y + y = 0, given that y = 2 sin x + 3 cos.x

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Q: Use a computer algebra system to evaluate (x2 – 2xy) dS. (Round your answer to two decimal places.)…

A: Here we solve the given calculus problem.

Q: The antiderivative of Cos(3x) is Blank 1 (use small letter no space)

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Q: Let f(x, y) = 2e sin(4) of д х of dy Check Answer

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Q: Given f(x,y) = e X cos y, Evaluate fx(0,2) cos 2 -sin 2

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Q: Given that f(x, y) - cos(x²) + 6e* sin y . Find fxyxyx · %3D

A: fx, y=x61+6y-cosx2+6exsiny Partially differentiating with respect to x, we get…

Q: Obtain the der a) cos(xy)=2y, find y'

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Q: (b) Determine J cos(x²) 2x dx by using substitution method.

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Q: Find y" at (2,4) for cos(x²y + 5) = 16. %3D

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Q: Determine cı and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y () = 0…

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Q: (1+cos y) dy y+sin y

A: To solve the integral, ∫(1+cos y)dyy+sin y, we need to use integration by substitution method. In…

Q: Given that: z = y sin(2x) + (1+x²)e* + cosx tan¬(y* + 1) In(y® + 137)

A: ∂z/∂x  is the partial differentiation of function z with respect to x, keeping other variables…

Q: Find the clerivative of Y. a) y = Sin3x t cos3 x %3D b) y = tan? (x³) c) y=4 sec (5x)

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Q: Cos Vt dt 3. Evaluate

A: The integration of the given integral is; Cos√t/√t.

Q: Find a trig substitution r = f(@) that makes 1 dr = cos 0 de. (V4+)3

A: Here we have to substitute x =f(θ)

Q: The integral . (cos(3x))'sin(3x)dr under the change of variable u = cos3r becomes v u'du. 9/29

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Q: Use Gaussian Quadrature (n = 3) to approximate f(x)dx, where: f(x) = (2.54 - sin0.32x)2 cos0.32x ,…

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.