Evaluate each of the following. a) So* sec²(x) tan°(x) dx b) , |x – 5| dx + c) Sx Vx? – 1 dx

Q: 1 2. Evaluate =dx using the trigonometric substitution x= 2 tan0. 2 Vx + 4

A: As per honor code, we will answer the first question for you. Please submit the other as a separate…

Q: b) S sin 2 x cos x dx

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Q: Q2/a) Find the integral f tan5x dx cos³x b) Find the integral cos*x dx 1-sinx

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Q: 1 |+tan¬(x), then x2 dy If y=cot-= dx

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Q: 2 6. dx (sin x – cos x)?

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Q: Recall that cos- arccos x. Find r1/2 e sin(cosx) dx. 0.

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Q: Find in each of the following. dx sin x 1. y = 1+cosx

A: We have to find the derivative

Q: 6. Identify the proper trigonometric substitution and then solve the integral 1 dx (x² + 1)²

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Q: 5. Assuming that (d/dx) (sin x) = cos x and (d/dx) (cos x) = - sin x, prove each of the following. d…

A: The quotient rule of differentiation states that uv'=u'v-v'uv2. (a) Write cot x=cos xsin x and use…

Q: Show that both y = sin x and y = cos x satisfy y" = -y.

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Q: d Q 3. Prove that tanx dx sec?x. =

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Q: 4- Find dy/dx for: a- y = sec?x – tan?x b- y = sec³ ( – x) %3D c- y = sin(tan(3x)) d- y = /1+ sin³…

A: NOTE- Since questions 1, 2, 3, 5 and 6 are incomplete, so solving question 4 only. Please submit the…

Q: T Cos x-sin x Jr x² dx So

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Q: 10. f sin x dx 25+cos²x

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Q: 8. Convert all expressions in (a-<) to a form A (x)+ B (x) dxteNote that A and B will vary from <ase…

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Q: If z=In/x2+y2 +- tan 2 then the numerical value of + is equal to..... dy? dx

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Q: Evaluate. d [arctan a – In ¤] dæ 1 1+#? 1 sec2 x sec² ¤ 1-x²

A: As we know that: The sum rule: f±g'=f'±g' The chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1…

Q: Evaluate ∫ a cos x dx and ∫ a sin x dx, where a is a constant.

A: Given∫a cos x dx

Q: bx + c Given tan 3 - In(x2 - 8x + 25) + 1 -dx %3D x2 - 8x + 25

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Q: Find d-/dx² at the given point without eliminating the parameter. x=0+ cos0 and y=1+sin0 ; 0 =a/6,

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Q: if y = a sin x Prove a +b CosX a cos + b %3D 2 (atb cosx) 11

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Q: Q: Evaluate: 2х -1 cos dx (1+x²

A: Solved below

Q: Which of these will represent u in the function * y= sin -1 Vx2 + 3x + 4? Sin-1 а. du V1-u?

A: Using definition of composite function.

Q: Consider the implicit function. e = sin (6x) Determine the formula for in terms of x. dy dx dy dx

A: Given: The implicit function ey=sin6x. To find: The formula for dydx in terms of x. Formula Used:…

Q: B) Find and if x sin 3z and y = tan 3z dx

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Q: Eliminate the parameter: x = cos3 t and y = sin3 t.

A: Given: x=cos3t                                               ..1y=sin3t…

Q: The amplitude A and period T of f(x)=5sin(4x) are..................... and ....................

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Q: (a) Find dy for dx = In (3x – 2) (tan 2x) -

A: Explanation of the solution is given below..

Q: The f xcos x² 1-sin x2 dx is

A: Given :

Q: Q57.a) Find if y=sin(tant) and t=cos(x) dx

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Q: 14. Find a) esin 2xdxb) J vanyt dx, using the substitution x= 2 tane. 15, Find a) fxe"-dx b) dx…

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Q: Demonstrate and derive the following Bernoulli's Equation. - 2y tan x = y² tan²x dx

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Q: al equation sin(t) with y( solution for this hen t belongs to ||

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Q: 7. Let f(x,y)= a) T 2 xsin y-y, find sin x+y Simplify and give exact value

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: 25. Assuming that (d/dx) (sin x) = cos x and (d/dx) (cos x) = - sin x, prove each of the following.…

A: Our Aim is to prove the derivative of the following:-(i) ddxtan (x)=sec2 (x)Proof⇒ddxsin (x)cos…

Q: dx 5) prove that sin x+c using method of trigonometric substitution. %3D

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Q: Q2: Evaluate: * Jx* sin(1- x)dx?

A: use substitution method to solve the integral

Q: FIND THE SECOND DERIVATIVE (y") OF THE FOLLOWING IN ITS SIMPLIFIED FORM (COMPLETE SOL'N): у%3D 3…

A: given that y=3 arccos1-x3+6x-x2 find the second derivative of y

Q: find dy /dx for the following 3 2 -1 Y3x'+Sin x+ Sin5X

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Q: a)- Find for, (x+ y)* = tan-14x + + Inlny !! dx

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Q: 1 dx J 3 sin x+4 cos x+3

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Q: In Va? + b² dx In x arc tan- Jo (x + a)² + b² where a and b are real.

A: We will prove the given identity by solving the integral using appropriate substitution.

Q: Let a be a constant. Evaluate 2 ((2* + 2² + a) sin(4x³) + 12a²)dx.

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Q: If y= cot"+ tan-1x?), then dy dx x2 Select one: 2х + 1+x*' 1-x4 2x O a. 2x O b. 1+x' 1+x? 2x Oc. 2x…

A: All given options are wrong. See the attachment

Q: Consider the implicit function. e' = sin (6x) Determine the formula for in terms of x. dy dx

A: Here we have to find the derivative.

Q: Prove that d/dx [cos x] = −sin x.

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Q: x2 sin3(x) Q.2\ Find dx if y = In cos(x*).V1+x/

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Q: B) Find and It x sin 3z and y= tan 3z dx

A: x=sin23xy=tan 3xWe need to find dydx and d2ydx2.

Q: 7. Find (a) y = (x* + 5x) cos 5x %3D dx

A: We can find the derivative using product rule as below

Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.