The sutiable substitution for evaluting csc'(x)cot5(x)dx is (a) u = tanx (b)u = cot x (c) u = cscx (d) u = secx (e) None a b O

Q: ind the slope of the tangent line to the curve 4 sin(x) + 5 cos(y) − 5sin(x)cos(y) + x = 3π at the…

A: To find the slope of the tangent line of 4sin x+5cos y-5sin xcos y+x=3π, differentiate it and…

Q: 4. y = 5 cos 4x, 3rd derivative 5. y = 3 tan 3x, 2nd derivative %3D 5. y = 6 csc x, 2nd derivative

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Q: cos x 3. y = tan (3x)cot (3x) 4. y = 1+sin x 5. y = arctan (3x5) 6. y = x arcsin x + V1- x²

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Q: tane cote +- = sin0 + cose %3D 9. Sece csce

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Q: luaté the lntegr sec2 x Vtan x xp= sec x . tanх + С 2ysec x + C 2/tan x + C

A: We will use substitution method to find the integral of given expression.

Q: tan x sec X 3 10 cos xdydx

A: Given : Double integral ∫0π/2∫0tan x sec x y3 cos10x dydx   To find : Evaluate the given double…

Q: 6. cos x(csc x secx) secx) cotx

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Q: cotx(secx-cos x)

A: We have to find  cotx (secx - cosx) We know that ,  cotx = cosx/sinx secx = 1/cosx  Then ,

Q: What is the integral of question 23 and why is the answer 0?

A: Let f(t)= t^4*tan t/(2+cos t)

Q: 2-sec2x: COS2X = COS X

A: Given query is to verify the identity

Q: If y=sin(sinx) show that y''+(tan x) y'cos2x=0

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Q: (cose+ tane) de / (sece + tan@sec2e) de cos e COS True (B) False

A: We have to find out

Q: Evaluate dy/dx at the point (π/2, π/2), if 2 sin^2 x + 1/2 cos y = (3 sin x)^11 . Mention all…

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Q: EX-15- Prove that : a) Sec-'x= Cos- ! b) Sin-' (-x)=-Sin-'x

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Q: 4. y = tan¬1(3x) cos 1 4x 5. y =

A: To determine the derivative of given functions. Here we will use the following formulas-…

Q: f y=sin(sinx) show that y'' +(tanx) y''+y cos2x=

A: Given that y=sinsinx To show that y''+tanxy'+ycos2x=0

Q: |12 sin(4x) cot(cos(4x)) dx

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Q: 2 tanx cotx – tanx=0

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Q: sin(-æ) = - %3D V2 tan(x) = – %3D cos(x) csc(x) cot(x)

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Q: 4. The 1" derivative of y : cotx a) xsec?x + tanx b) xsecx - tanx c) cot x + xcsc'x d) cot x - xcscx

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Q: Evaluate S tan'x sec'x dx sec x 2 secx sin x - 2 sin'x + sin'x +C 3 3 Option 1 O Option 2 - cos'x +…

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Q: Find the exact value of sin(x - y) if sin x = 3 ≤ y ≤ 2. on ≤x≤ and sin y=-3 on

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Q: Find sine half range for f(x) = \cos x for -1<x<1 COSX for < x < 0. f(x) { COSX for 0 < x < .

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Q: Subject find derivatines of the first derivatives in volving differe and questients? 4 %3D COSX tanx…

A: Derivatives of function

Q: (a) Show that tan x = dx sec?x using quotient rule.

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Q: S tanx 1+ COS X JX

A: Given problem:-  ∫tan(x)dx/(1+cos4(x))

Q: 12. Find the first derivative of y = 2cos(2 + x*). A. -4x sin (2 + x2) B. 4x cos (2 + x*) C. x sin…

A: Questiopn no. 12,Given,           y=2cos2+x2To find : The first derivative of the function.

Q: Si cos°(3x)sin (3x) – cos (3x) sin°(3x) dx

A: First we common out cos7(3x) sin7(3x) and then apply the formula cos2(3x)-sin2(3x)=cos(6x)

Q: Va2-x² Y=Arc sin + а

A: Differentiate wrt x

Q: Find the equation of the tangent line to the astroid x = cos° (0), y = sin³ (0) at 0 = 5. (Express…

A: The given equation of the astroid:x=cos3θ and y=sin3θWe need to find the tangent line to the astroid…

Q: 12 tan (4.x) sec (4x) dx S cos(11x) sin(2r) dx COS

A: Given that integration and we solve this integration by using general formulas of integration. Here…

Q: Integrate cosx cos (x-a)

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Q: cos^2x+sin^2x/cos^2x=

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Q: verify tan(y)/csc(y)=1/cos(y)−1/sec(y)

A: Given data:     The given trigonometric expression is: tan(y)/csc(y) =1/cos(y) -1/sec(y).     To…

Q: 3 cos xdx 1-sinx

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Q: 1+ cosx + sinx sinx 1+cos X 2sec x 2csc x 2csc 2x 2sec 2x

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Q: Compute (sin (x)) dx cos'x 3 sin' x cos x O Not listed here 3 sin? x 3 sin x cos x

A: Given query is to find the derivative of the expression.

Q: sin(2x) dx cos(2x)+5 2x dx V3x +1 4 sec2(2x) dx ! 3(1-tan 2x)

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Q: 1 (tan x + cot х) sec x %D 1/cosx 1/sinx 1

A: Given query is to find the correct option for the expression.

Q: y = sin(2x) sin(x) + cos ( 2x) cos (x) COS %3D

A: Using the formula of cos(A-B)=cosAcosB+sinAsinB. Explanation is given below..

Q: the slope of the tangent. line to: the graph of y=XT COSXY the point (0,1)? What is of: 4=XT COSメ

A: Given: y=x+cosxy

Q: do sin 0 – cos 0 cos 0

A: The given integral is ∫dθsinθ-cosθ

Q: Find sine half range for f(x) = \cos x for -t< a <n %3D cosx for f(x) for 0<x <n. cosx

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Q: Find generul solution ý +y tan (x) = see (X) - sec %3D

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Q: 1+ cosx + sinx sinx 1+cos x 2sec x 2csc x 2csc 2x 2sec 2x X.

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Q: d. tion to prove that (cscx) dx = – CSC X COt x. 86. Use the quotient rule and the derivatives of…

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Q: Show complete solution. Determine the slope of the tangent line to the graph of the equation ey =…

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Q: If sinx = siny = a and cosx = cosy = b,then cos(x-y) is

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Q: 04.) Show that y = (sin x +cos x) sec x = sec² x

A: Given inequality does not equal. See the attachment

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.