BE Automobile Engineering छमाही १ (इंजीनियरिंग) - University of Mumbai Question Bank Solutions

Obtain tan 5𝜽 in terms of tan 𝜽 & show that `1-10tan^2  x/10+5tan^4  x/10=0`

If y=etan_1x. prove that `(1+x^2)yn+2[2(n+1)x-1]y_n+1+n(n+1)y_n=0`

Find tanhx if 5sinhx-coshx = 5 

Separate into real and imaginary parts of cos`"^-1((3i)/4)` 

Considering only principal values separate into real and imaginary parts

`i^((log)(i+1))`

Find the n^th derivative of `x^3/((x+1)(x-2))`

If `u=r^2cos2theta, v=r^2sin2theta. "find"(del(u,v))/(del(r,theta))`

Find the nth derivative of cos 5x.cos 3x.cos x.

Evaluate : `lim_(x->0)((2x+1)/(x+1))^(1/x)`

Prove that `log((a+ib)/(a-ib))=2itan^(-1)  b/a      &    cos[ilog((a+ib)/(a-ib))=(a^2-b^2)/(a^2+b^2)]`

Evaluate `lim_(x->0) sinx log x.`

Find the n^th derivative of y=e^ax cos2 x sin x.

Find nth derivative of `1/(x^2+a^2.`

Find all values of `(1+i)^(1/3)` & show that their continued
Product is (1+i).

Express `(2x^3+3x^2-8x+7)` in terms of (x-2) using taylor'r series. 

Prove that `tan_1 x=x-x^3/3+x^5/5+.............`

If y=(x+√x²-1 ,Prove that

`(x^2-1)y_(n+2)+(2n+1)xy_(n+1)+(n^2-m^2)y_n=0`

Using De Moivre’s theorem prove that]

`cos^6theta-sin^6theta=1/16(cos6theta+15cos2theta)`

Solve  `x^4-x^3+x^2-x+1=0.`

If `y=e^(tan^(-1)x)`.Prove that

`(1+x^2)y_(n+2)+[2(n+1)x-1]y_(n+1)+n(n+1)y_n=0`