Question

PLEASE SOLVE THIS ...

Answer 1

please refer to the attachment

Answer 2

#Hey there !!
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..........| sinx cosx tanx |
f(x) = | x³___ x² ___x |
..........| 2 x ___1___ 1 |

◆solving this determinant :

f(x) = sinx(x²-x) -cosx(x³-2x²) +tanx(x³-2x³)

=x²sinx -xsinx -x³cosx +2x²cosx+x³tanx-2x³tanx

f(x)/x² = sinx -xsinx/x -cosx +2cosx -xtanx

>>now applying limit

=> lim f(x)/x²
x--> 0

=> lim { sinx - sinx/x -xcosx +2cosx -xtanx}
x-->0

now applying limits separately :

we get,

=> ( 0 - 1 - 0 + 2 -0 ) = 1

so , lim f(x)/x² = 1
x-->0

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HOPE IT WILL HELP YOU