Limits

BITSAT 2015 Tutorials › Co-ordinate Geometry questions › Limits

evaluate a,b,c,d
if lim xâ†’âˆž (âˆšx⁴+ax³+3x²+bx+2)-(âˆšx⁴+2x³-cx²+3x-d=4

#Mathematics #Co-ordinate Geometry

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6 Answers

62

Lokesh Verma ·2009-03-19 06:25:51

rationalized?

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106

Asish Mahapatra ·2009-03-19 06:28:11

lim(xâ†’âˆž) (√x⁴+ax³+3x²+bx+2 - √x⁴+2x³-cx²+3x-d)(√x⁴+ax³+3x²+bx+2 + √x⁴+2x³-cx²+3x-d)/√x⁴+ax³+3x²+bx+2 + √x⁴+2x³-cx²+3x-d)

= lim(xâ†’âˆž) [(a-2)x³ + (3+c)x² + (b-3)x + 2+d]/√x⁴+ax³+3x²+bx+2 + √x⁴+2x³-cx²+3x-d)

now as lim exists and equal to 4 and the highest deg of numerator = 3 while of denominator is 2 ... So, a-2 = 0 ==> a=2

(3+c)/2 = 4 ==> c = 5

now u have to calculate valus of b and d such that √x⁴+ax³+3x²+bx+2 and √x⁴+2x³-cx²+3x-d are defined

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1

Optimus Prime ·2009-03-19 06:55:59

after that

(3+c)x²+(b-3)x+(2+d)/ denominator
dividing numerator and denominator by x² we get,

(3+c)+(b-3)/x + (2+d)/x² /denominator

3+c/2=4

c=5
a=2

b and d are any nos

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1

Optimus Prime ·2009-03-19 07:01:37

are u guys getting it as c=5 a=2 and b and d any nos?

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62

Lokesh Verma ·2009-03-19 07:02:05

cool work guys :)

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Optimus Prime ·2009-03-19 07:02:46

thanks

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