8) Find the dexivative of fex) - sinx cos x, Write your answer Single term. as a

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

A: Given:sinx=0.3

Q: Q5. If coshx = csc20, prove that 0 = n+ cothe¯. [Hint: use identity sin(2a + 2n)] %3D

A: given that                                                                             coshx=csc2θ…

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

A:

Q: i) Show that the real solution of tanh x = cosechx can be written in the form x = In u + vu. Find an…

A: Note:  As per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: find the four non zero terms in the maclaurin serise for sin h-lx

A: Formula Used: We will need following binomial expansion:

Q: 7. Show that sin E + x) = G+x): = -cosx.

A: Introduction :

Q: b) cos(-z)=?

A: In the question we have to find the angle of cosine which is lying in third quadrant as cosine is…

Q: tan 0 de equals to : 1+sece In |1+tane|+c In |1+sece|+c O (tane)^2/2+c -In |1+cose|+c

A:

Q: find the value of cE CoB] for flx)= that satisfy value theorem. mean

A:

Q: (-1) cos[cosh (In ")]dr 4.

A:

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

A:

Q: The integral ¹S. 01-fese csc ³0 de sin² sin ²0 de = [sec³ sec ³0 de + cos² cos²0 de dx (x²+4)² can…

A: We have to solve Integral

Q: cos" xdx :0. 6. If n is a positive odd integer, prove that

A:

Q: Use the addition formulas for sinh x and cosh x to prove tanh u + tanh v tanh(u + v) = 1+ tanh u…

A:

Q: Prove using the IVT. tan-1x = cos-1x has a solution.

A: Given :                      tan-1 x = cos-1 xSolve :                     tan-1 x = cos-1 x…

Q: 1. If z = sin2+In^, find the value of x- +y X

A:

Q: Obtain graphically an approximate value of the lowest root of cos x cosh x =- 1.

A: The equation cosxcoshx=-1 regulates the frequency of vibration of a cantilever. We must first…

Q: (3.2 cos 2x+2 -dx. 1.8 1+ In x Use NINT on the calculator to evaluate:

A: We have to evaluate ∫1.83.2 cos 2x + 21 + ln x dx.

Q: 2 cos(5x) – 5 x² – 2 lim sin(3x) – x² – 3x - - (Write your answer in the given box)

A: We will use L'Hopital rule

Q: E prove that - Cotx + C %3D 2 |- Cos?x +Sinx

A:

Q: 3. Are reduction formulas needed to evaluate sin x cos? x dx? Why or why not?

A:

Q: 3. sin 3z cos 5z dr

A: Here we have to evaluate I=∫sin3xcos5xdx

Q: 40 a) Find sin' xcos' xdx by using substitution u = cosx.

A:

Q: Find the first 3 Zerms o Sinx et a =?

A:

Q: If tanh(x)=5/13, what is the sinh(x)?

A: Answer is sinhx=5/12. Explanation is given below..

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

A:

Q: a) By expanding sin (2x + x) and using double angle formulae, show that sin 3x = 3 sin x - 4 sin°x.…

A: Evaluation of the definite Integral

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

A:

Q: .If z = e-(sin x + cos y), show that a²z a2z az ax2 ду? at

A: Given - z = e^-t( sinx + cosy)

Q: (4) |sin² 0 cos0 d0

A:

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

A:

Q: state what method applies and how one applies it, but do not evaluate the integral:

A: Given integral is We will evaluate the integral by substitution method.

Q: Evaluate the integral: 3 X sin ³ COS 3 3 X col 3

A: Solved below.

Q: 2. Show that y = ce sin

A:

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

A:

Q: 5) prove that = sin 'x +e using method of trigonometric substitution.

A: To Prove- Prove that ∫dx1 - x2 = sin-1x + c using method of trigonometric substitution.

Q: Can the Intermediate Value Theorem be used to prove that the equation 9 2(r + 9) sin*(x) – 4 cos"(x)…

A:

Q: Use the addition formulas to deriv TT 31. cos(x - sin x 2

A: Prove that cos( x  - π/2 ) = sinx Here we use general formula : cos( A - B ) = cosA×cosB + sinA×…

Q: Derve the Jrmula Cosh 2. Find dy Sor Sin ソー X-/ xp

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: -Tt/2 Evaluate using Wallis' Formula: 7 sin5 x cos6 x dx

A:

Q: Show that, for real values of x, 3 sin x f(x) 2 + cos x cannot have a value greater than 3 or a…

A: To show that the minimum and maximum value of the function is -√3 and √3

Q: Show that : |sin x |= CoS nX Σ n2 even 414 2/7

A:

Q: Use the double-angle formula cos 2x = 2 cos x – 1 to evaluate the integral 1 1+ cos 2x dx

A: The given integral is ∫11+cos2xdx

Q: Use a computer algebra system  to find  integral sin 5 x cos 2 x   dx

A: To find the integral

Q: Determine the period as requested. 5) Feriod of y 5 sin 4x A) 4 C)2 -1/2

A: In this question, we want to find the period of the given function.

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: