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By using properties of determinats. Prov...

By using properties of determinats. Prove that-
`|(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4)|` = `(5x + 4) (x - 4)^2`

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By using properties of determinants. Show that: (i) |(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4)|=(5x-4)(4-x)^2 (ii) |(y+k,y,y),(y,y+k,y),(y,y,y+k)|=k^2(3y+k)

Solve : |(x+4, 2x,2x),(2x , x+4, 2x),(2x, 2x, x+4)| = 0

By using properties of determinants , show that : (i) {:|( x+4, 2x, 2x),( 2x,x+4, 2x),( 2x,2x, x+4) |:}=( 5x +4) (4-x)^(2) ( ii) {:|( y+k , y , y ),( y,y+ k , y ),( y,y , y+k ) |:} =k^(2) ( 3y +k )

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If |(x-4,2x,2x),(2x,x-4,2x),(2x,2x,x-4)|=(A+Bx)(x-A)^2 then the ordered pair (A,B) is equal to

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If a,b,c are in A.P. then the determinant {:|( x+2,x+3,x+2a),( x+3,x+4,x+2b),( x+4,x+5,x+2c)|:} is

UNITED BOOK HOUSE-MISCELLANEOUS EXERCISE-EXERCISE
  1. Solve : cos^-1 x - sin^-1 x = cos^-1 (x sqrt3).

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  2. If phi = tan^-1 (xsqrt3)/(2k-x) and theta (2x-k)/(ksqrt3), then show t...

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  3. By using properties of determinats. Prove that- |(x+4,2x,2x),(2x,x+4...

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  4. By using properties of determinats. Prove that- |(1,1+x,1+x+y),(2,3+...

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  5. By using properties of determinats. Prove that- |(sintheta,costheta,...

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  6. Let X = [(3,2,5),(4,1,3),(0,6,-7):}] express X as sum of two matrics s...

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  7. If [(2,-1),(1,0),(-3,4):}]xxP= [(-1,-8,-10),(1,-2,-5),(9,22,15):}], fi...

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  8. Prove that: underset(xrarrinfty)lim sqrtx (sqrt(x+3) - sqrtx)= 3/2

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  9. Prove that:underset(x rarr0)lim ((x-1+cosx)/(x))^(1/x) = e^(-1/2)

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  10. Prove that: underset(xrarrinfty)lim ((x+5)/(x+1))^x = e^4

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  11. Prove that: underset(xrarrpi/2)lim (1+cosx)^(3secx) = e^3

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  12. Prove that: underset(xrarr0)lim ([1+3x]^((x+3)/x))= e^9

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  13. Evaluate the following limits: underset(x rarr0)lim(xe^x - log(x+1))/(...

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  14. Evaluate the following limits: underset(x rarr0)lim[tan(pi/4+x)]^(1/x)

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  15. Evaluate the following limits: underset(x rarr0)lim(sinx + cos x)^(1/x...

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  16. Evaluate the following limits: underset(x rarr0)limsinlog(1+x)/log(sin...

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  17. It g(x) is the inverse of f(x) and f(X) = (1+x^3)^-1, show that g'(x) ...

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  18. Find the differential coefficients of the folloiwng functions: x^x

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  19. Find form 1st principle the differential coefficients of the folloiwng...

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  20. Find form 1st principle the differential coefficients of the folloiwng...

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