Consider the fune tion fa)- In[ax- b an tb] where c= ? -6 bi 2ab ind f' ()

Q: Prove that the equation sinx = 0.3 has at least one solution in the interval (o, ~).

A: Given:sinx=0.3

Q: 2.) Evaluate using wallis formula 1-x² dx and let x= sine

A: Given ∫01x41-x2dx By using 1-sin2(x)=cos2x And Wallis formula…

Q: 31) Find tue derivetive of tue funcrion heae) = I Sinh 2x -7X 4

A: For derivatives we just apply differentiation both side.

Q: Q3) Ify = in[sec 8 + tan 8) find

A:

Q: Apply Maclaurln's Serles to Show (-1)*-1,2=-2) 2(n – 1)1 cos X=

A:

Q: If n is an odd natural number prove that I =, xsinnx dx = sinx 2.

A: Consider the given: It is given that n is an odd natural number, Take n = 1,Substituting n=1 and…

Q: Prove that Va2 + 4 sin ( sec %3D V2 +4

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: ) Prove that 2+sinZA Cos A-SinA

A: To Prove: cos3A-sin3AcosA-sinA=2+sin2A2

Q: Integrate sin" uelog(cosu) . Where n=666

A:

Q: find and classi f1 extrem um points of the func tion flriy)exěsing

A: First we will find all critical points.

Q: Prove the trigometr 1-Cos (o) Secco) I +seclo) Sina co)

A:

Q: Show that sin mx cos nx dx = 0 for positive integers m and n: i using the primitive, ii using…

A:

Q: =-i In (izt Ji-z2?) Sin 군 tan 군 = 늑In

A:

Q: Q4:B/Simplify [cos 20-i sin2018 [cos 30+ i sin30 1² [cos 40+ i sin40 ]³[cos 20-i sin2015 using De…

A:

Q: if f(2) = zsin(z) -1 defined on the interval (2. 3] then es using False-Position method equals [x in…

A:

Q: Show that cosh iθ = cos θ,

A: We know that  coshx=ex+e-x2 and by Euler's theorem, eix=cosx+isinxe-ix=cos-x+isin-x=cosx-isinx We…

Q: Find the areg between Ye CosX an d y--SinX trom o tr .

A:

Q: Prove the following equation : Cosh(3 x) = 4 cosh³(x) – 3cosh(x)

A:

Q: కషిద్టి చవీ / tangent s lope rosin (20) when Jot 5 2) 653 3. not of the above

A:

Q: esirq) . cos(q) dq 5x/2

A:

Q: find: de So 2-cose using sediment theorem

A: Solution :-

Q: Evaluate fi' sin(21*)dt

A:

Q: 5. If coshx = csc20, prove that 0 = n+ cothe¬x. [Hint: use identity sin(2a + 2n)]

A:

Q: Use linear approximations to estimate the following. 1. sin 9/4

A:

Q: e in Q2, find Sin (2e) with 6 If csce -6,

A:

Q: Prove That 4 Sin ³²A - CoS 3 A +4 Cas³ A - Sin 3 A = 3 Siny A

A: We need to prove: 4sin3A.cos3A+4cos3A.sin3A=3sin4A

Q: Integrate sin" uelor (cosu) . Where n=540

A:

Q: Show that the equation 2x + cos(x) = 1 has exactly one root. (IVT and Rolle's Theorem)

A:

Q: Suppose that π≤θ≤3π/2, tan(θ)=6/12, find sin(θ)=______. (round to 3 decimal places)

A:

Q: Prove 3n - T, 2 sin? x – sinx cosx – 2 cos? x=0 in has five root's Hint. Intermediate value theorem

A: Corollary of Intermediate value theorem :- If a continuous function has values of opposite sign…

Q: Assuming that |a| < 1, find the value of cosh ax dr. cosh x

A: It is given that,a&lt;1, we have to find the value of              ∫0∞coshaxcoshxdx

Q: Prove (05t - sin 4t tos?t

A:

Q: 35. Use property IV of Appendix A to verify that 1 L'{arctan(a/s)} =sin at

A:

Q: @H-w/ prove that cosiz=coshz

A: We have to prove by using cosiz and coshz formulae.

Q: Find a series of cosines of multiples of x which will represent (x sinx ) in the interval (O, x) and…

A: Let's expand x cos(x ) , xcosx=x1-x22!+x44!-x66!+...=x-x32!+x54!-x76!+...             in 0,x To show…

Q: Prove that 2 arcsin (x) = arccos (1-2x2) for XE (0, ) Hint: you may want to differentiate these…

A: We can prove these by two ways . First is by using derivatives of functions. And second by using…

Q: 12. Write an éxpression that gives all sölutions to the equation. COS X - SIn x 3= 2.

A:

Q: Prove that osIl" + sini = tan s 56° cas 11-sinll %3D

A: -To show:cos11o+sin11ocos11o-sin11o=tan56oBasic formula needed:-tan(A+B)=tanA+tanB1-tanA.tanB…

Q: 9 Prove Sen 4t 4 cos3t sint-sin3t cos t.

A:

Q: What is the integrable form of sin-cos-sino do?

A:

Q: How do you evaluate ∫ sinmx cosnx dx if m is odd? What if nis odd? What if m and n are both even?

A: If n is odd use substitution with u=sin x, du=cos xdx and convert the remaining factors of…

Q: /2 Evaluate using Wallis' Formula: sin5 x cos6 x dx

A:

Q: Let fla)= é cosx, s** %3D Express your answers in exact form.

A:

Q: sec 1.)S Intanßtanß dß

A:

Q: Suppose that π≤θ≤3π/2, tan(θ)=10/7, find sin(θ)=______. (round to 3 decimal places)

A: The given problem is solved below details.

Q: Prove that : 1. Sinhx= In(x+x² +1)

A:

Q: Define Rolle's Theorem. With the help of Mathematica, show the applicability of the theorem en…

A: Rolle's Theorem: Let a &lt; b If f be a continuous function on the closed interval [a, b]  and…

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.