lim_x 0 0.05em ax^2e^x-b log_e ⁡ (1+x )+ cxe^-xx^2 sin ⁡x=1 then 16(a^2+b^2+c^2) is equal to

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Accepted Answer

Correct answer: 81. (81) ax^2 ⁡(1+x+ x^22 !+ x^33 !+ …)-b(x- x^22+ x^33- … …) lim_x 0 0.05em + cx(1-x+ x^2x !- x^33 !+ … …)x^3 sin ⁡xx= lim_x 0.05em (c-b )x+( b2-c+a)x^2+(a- b3+ c2)x^3+ … …x^3 =1c-b=0 , b2-c+a=0a- b3+ c2=1a= 34b=c= 32a^2+b^2+c^2= 916+ 94+ 9416(a^2+b^2+c^2)=81

$lim_{x \to 0} \frac{a x ^{2} e ^{x} - b log _{e} ( 1 + x ) + cx e ^{- x}}{x ^{2} sin x} = 1 then 16 (a^{2} + b^{2} + c^{2}) is equal to$

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