e* sec (e* +1)dx tanle* +1

Q: sinh x 1+ cosh x

A: sinh x1+cosh x

Q: (Integral sign) tan^4 x sec^6 x dx

A:

Q: If tanx=sinha prove that a=ln(secx+tanx

A:

Q: ∫sin(8x)sin(x)dx

A: Solution:- =∫sin8xsinxdx Applying the Product-to-sum formulas,   sinxsiny=12[cosx-y-cosx+y]…

Q: tan"x jun's de - | tan"-x dx (n 1) n- 1 tan x sec" r sec x dx (n 1) n- 1

A:

Q: VT (2x)[sin (2x²)] cos (x²) your exact-value result. Evaluate dx. Show complete pencil-and-paper…

A:

Q: find the given limits

A: The given limits,

Q: lim x approaches zero, sin4x/sin3x

A: Given,

Q: rin 2 e2# sec-"(e")dr

A: Solution

Q: y=-sec^-2 (In x)

A:

Q: 18. [ tan(In x)

A:

Q: (tan x) = fu. v dx = (sin x) = | -=-=dx = (cos x) = fe" dx = | (arcsinx) = sec x tan x dx = secx tan…

A: We have to find out derivative and integral

Q: ftan (x}sec"(x)dx Scot (x)csc°(x)dx Ssin (x)cos°(x)dx

A:

Q: 1 -dx cos.x-1 2) Integrate

A:

Q: 9-メ dx

A: Sum rule of integration-

Q: ) Isinx-sinyls lx-y!

A:

Q: sin x Show that secx = cosx - then use the identity to derive the basic integration rule f secx dx =…

A: RHS=sinxcosx+cosx1+sinx=sinx1+sinx+cos2xcosx1+sinx=sinx+sin2x+cos2xcosx1+sinx=sinx+1cosx1+sinx=1cosx…

Q: limit Sin @2@) 0so ton Cs0)

A: solution

Q: = cosx (sinx). 2. Find the Fourier series on -≤x≤π for f(x) =

A: Given the function fx=cosxsin2x, -π≤x≤π

Q: (Integral sign) tan^2 x cos^3 x dx

A: The given integral is

Q: sechx+cshx b) prove that e2x cshx-sechx

A:

Q: S(sec x tan x – 4x³)dx = - o tan x + х* + с sec x x4 + c sec x + x4 + c - sec x + x* + c - sec x x4…

A: Some of the properties of integration ∫f(x)+g(x)dx=∫f(x) dx+∫g(x) dx ∫xn dx=xn+1n+1+C ∫ (sec x tan…

Q: Integration of b/1-sinbx dx

A:

Q: limx>0 sin-1x/x

A: So, now we apply L' hospital rule to evaluate the given function. Because if we directly apply the…

Q: ‚arcsin(1+x²)] y'of y = In cscya

A: Given y=lnearcsin1+x2cscxWe need to find y'

Q: 1+ tanx log prove that = sec2x dx y 1- tanx

A: Giveny=log1+tanx1-tanx

Q: Show that

A: Given: verify that secx=sinxcosx+cosx1+sinx for verifying given identity, we solve left hand side…

Q: feois Pdf find

A: f(x) is the probability density function if the area under the curve is one and f(x)>0

Q: integration of sin2x.cos3x dx

A:

Q: (5) sinh 2x = 2.sinh x.coshx %3D

A: (5)To prove the following identity sinh(2x) = 2·sinh(x)·cosh(x)

Q: ldx on the graph y sec x? + y? = cos2x at point (1, 2).

A:

Q: [sec² x (1 + tanx) Vtan² x – 9 tan* x| dx

A: Formulae used:…

Q: Intergal of (sinh x) / (cosh x + 6) dx

A: To find  Integration of (sinh x) / (cosh x + 6) dx

Q: Non Homogeneous LDE yIII  -  yII  =  3  + sin x

A: Given differential equation is y'''−y''=3+sinx. We have to find the general solution of the given…

Q: Arcsinx-sinx 1. lim x→0 (1-cos2x)sin2x 2-2cosx-xln(1+x) 2. lim x→0 x sin² x

A: 1)

Q: 2 *sinh“ x – sinh x+ cosh x dr -dx cosh¯ x

A:

Q: sinh- x = In 2.

A:

Q: 1. ,sinx cosxdx

A:

Q: solve using L'Hopital's Rule 3.  Lim    (ex + e-x  - x2 - 2) / (sin2x - x2)    x->0

A: L'Hopital's Rule: The rule is applicable when the value of the limit function limx→af(x)g(x) is…

Q: INTEGRATION OF 1/1+TANX

A:

Q: tanx – lim 0 Cos[1 – –

A: Given, -limx→0cos1-tanxx

Q: (3 sin x - sin 3x) dx

A: To integrate: ∫(3sin(x)-sin(3x))dx Solution: We know,∫sin(ax)dx=-1acos(ax)+C Using above standard…

Q: -1 -sec"(x) =: dx -csc"(x)= Explain why the modulus x Given that and dx is needed here.

A: Definition used -                                        ddxsecx =secxtanx…

Q: x+13 dx х+4

A: 1) Evaluate: ∫3x2+14x+13x+4dx

Q: sinh (2.Inx) n(coshx+Sinhx)+in(cashx-sinh x).

A: We have to rewrite the given expression by using the exponents.

Q: acrsin x:! csc-1 x: arccos x: sec-1 arctan x: cot-lx: : [0, T] :: [0, 플] : (- 1 : (0, 27] :: [-플, 이…

A:

Q: Beta Function 27 dx (*+ 1) Prove that

A: The given problem is to evaluate the given beta function integral.

Q: integral sin -1 x dx

A: Given Data The integral is ꭍsin-1xdx.   Let,

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.