E. DIFFERENTIATION Obtain the derivative of the following functions: y = Vx² (2x – a²)

Q: In the integral, cos?rsin2tdt , the correct u using general power formula is;

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Q: x--x+1 Evaluate: dx A 2,½_2,½-22+c 3 B 2 2 2

A: We have to find out the solutions

Q: Using the trapezoid rule and 1 rectangle, the integral fo dx is approximated by This is an • because...

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Q: |(3x + 1)2dx = Blank 1 (use small letter, no space) Evaluate: Blank 1 Add your answer

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Q: tan an Evaluate: 1+2512

A: Follow the procedure given below.

Q: Suppose a hot cup of coffee is left on a kitchen counter. If the temperature in °F after t hours is ...

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Q: Evaluate: ) ²dx secx- tanx

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Q: 2x2 + 2x+1 dx. Evaluate: e х+1 x2 (A 2 *+ In/x+1| +C B x² + In|x + 1| + C (x²+x+1 x+1 n|x+1| + C e 1...

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Q: 2w2+9w+1 dw is the same as w+4 2w +1+ dw w+4 B w+4 Mp MP 67 2w +17- W+ 4 None

A: We want to find correct answer from the given options. 

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Q: If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = f(x)/g(x). %3D %...

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Q: Question 11 dx 4+e (A) 4+e* (B) e ot D 4e*+1 E) None

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Q: If (Mesin(2) dx = e°sin(2») + C, then the M is equal to

A: On solving this we will get

Q: tan ( tan3x) dx Evaluate: cos?3x

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Q: dx 5+ x2 хах 5+ x2 5+ x2

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Q: csc2tdt In csc2t- cot2t +C A) True False

A: topic - indefinite integral

Q: Svar- 8x – 16 dx=2 x-2dx - 2 A) True B False

A: To simplify the integral.

Q: derivative of the fun x + 2 y = e y' = %3D

A: We are asked to find the derivatives of the function.

Q: Determine the roots of the following simultaneous nonlinear equations using Newtor Raphson Method, t...

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Q: IX. sin (2x)dx by using walli's formula. a is equal to ? 29. A.0 В.1 C.2 D.pi/2 The definite integra...

A: Let's find. 

Q: sin³ydy 1+ cosy (A) 1+ cosy B) 1- cosy с) siny D sin3y E) None

A: To find out the correct u to evaluate the integration. 

Q: The antiderivative of Cos(3x) jis

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Q: [sin(Inx?) ]²dx Which of the following is equivalent to :? sin(Inx14) dx A sin2( Inx 14) dx ® / B si...

A: ∫sinlnx7 2dxx

Q: Find the particular solution to the differential equation y' = (6xy)2 that passes through 1, − 1 ...

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Q: Solve the initial-value problem starting from y0 = 10. dy dt = −6y y =     At what positive time doe...

A: We need to solve the given separable differential equation

Q: If sin(t) = and t is in quadrant II, find cos(t), sec(t), csc(t), tan(t), cot(t). cos(t) %3D csc(t) ...

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Q: sin 2 tsin2tdt A sint 3 B sin 21 cost D sin21 E None

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Q: sin 2 rsin2tdt A sint B sin 21 cost D sin2t E None

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Q: dx 4+e=* A 4+e-* В D 4e+1 E) None

A: We have to find the integral

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. + 2)3/2, 2 < y <...

A: To find the exact area of the surface

Q: Evaluate: (3x + 1)*dx = Blank 1 (use small letter, no space) S(3x+1°dx,

A: Given  ∫(3x+1)2dx Formula: ∫(ax+b)ndx = n(ax+b)n-1.(a)

Q: f [Mesin(2x) dx = e$in(2x) + C, then the M is equal to- If

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Q: To evaluate the integral expression / sin -1(Vx ) dv, using simple substitution dv =f (x)dx_ Determi...

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Q: In order to evaluate the integral expression J In(sin(x))dv using simple substitution, dv =f (x)dx_ ...

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Q: company's profits if marginal profit is​ $0

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Q: Which of the following is a solution of the given initial-value problem? y'+ (tan(x))y = 5 cos 2(x);...

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Q: The volume V =ar° of a spherical balloon changes with the radius. a. At what rate (ft /ft) does the ...

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Q: Which of the following is equivalent to the integrand of ((sin(Inx7))? Which of the following is equ...

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Q: Improper Integrals w/ Partial fractions, Integration by parts and u - su L y e-3y dy Зу 11.

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

Q: The integral csc(0.5) dx is equal to A 2ln|csc(0.5x) – cot(0.5x)| + C ®2ln/tanh(0.5x)| +C (c) 4tan-l...

A: We have to find the integral

Q: Which of the following integration expression can't be transformed into integral of power 2dx A 4+3x...

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Q: Evaluate: tan(4x +3)dx A 4 A -In |cos (4x + 3)|+c B -In |sin(4x + 3)|+C 1 (c) -In |csc (4x+3)|+C D -...

A: integration

Q: Consider the following function: f (x) = (x- 4)(x+2) (x +4)(x + 2) i. For what values of x is f(x) c...

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Q: A function F (x) is called an antiderivative of a function f (x), if F(x)=f (x) B F(x)=f (x) F(x) =f...

A: topic - derivative and integration

Q: Instructions: Determine the derivative of the ff. functions 1. y = 6x4 + 7x³ - 8x² + 9x - 10 2. y = ...

A: According to guidelines we can solve only first 3 subpart. Please resubmit the others. Thank you.

Q: If s(x)dx=+C, then f (x): -3 x3 x4 А) True B False

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Q: A manufacturer produces bolts of a fabric with a fixed width. The quantity q of this fabric (measure...

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Q: Given Cost and Revenue functions C(q)=q3−9q2+56q+5000 and R(q)=−3q2+2600q​, what is the marginal cos...

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Q: tan( tan3x)dx Evaluate: cos²3x A 3 -In sec(tan3x)| + C B -n|cos( tan3x)| + C In|cos (tan3x)| +C (D D...

A: the given integral,      ∫tan(tan 3x)dxcos23x

Q: 4y+4(4x-5y)-7+9(3-7y)

A: