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# Tutor profile: Vijay K.

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Vijay K.
Mathematics Tutor for Seven Years
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## Questions

### Subject:Pre-Calculus

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Question:

Given the function f(x)=2x^2-3x calculate (f(a+h) - f(a)) /h

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Vijay K.

f(x)=2x^2-3x (f(a+h) - f(a)) /h (2(a+h)^2-3(a+h)-(2a^2-3a))/h (2(a^2+2ah+h^2)-3a-3h-2a^2+3a)/h (2a^2+2h^2+2ah-3a-3h-2a^2+3a)/h (2h^2+2ah-3h)/h h(2h+2a-3)/h 2h+2a-3

### Subject:Trigonometry

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Question:

Find the solutions of equation that are in the interval 0,pi/2]. tan 6x=tan 3x x=..? If the answer is x=2pi/3 then how does the answer become pi/3

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Vijay K.

tan 6x =tan 3x [0,pi/2] tan 6x -tan 3x =0 (Sin 6x /cos 6x)- (sin 3x /cos 3x) =0 ((Sin 6x* cos 3x)/(cos 6x cos 3x)) -((sin 3x cos 6x)/(cos 6x cos 3x)) =0 ((Sin 6x cos 3x) -(sin 3x cos 6x))/(cos 6x cos 3x))=0 Now, Sin A cos B - Sin B cos A= Sin (A-B) (Sin(6x-3x))/(cos 6x cos 3x) =0 Sin 3x =0 3x=2n pi or 3x= pi+2n pi x=2n pi/3 or x = pi/3+2n pi /3 Now, interval given is [0,pi/2] x=pi/3 and x=0

### Subject:Algebra

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Question:

Solve for x: 2x=sqrt(4x+15)

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Vijay K.

2x= sqrt(4x+15) squaring both sides 4x^2=4x+15 or, 4x^2-4x-15=0 4x^2-10x+6x-15=0 2x(2x-5)+3(2x-5)=0 (2x-5)(2x+3)=0 Hence, (2x-5)=0 or x=5/2 or, (2x+3)=0 or x=-3/2 Check:- 2(5/2)=sqrt((4(5/2) +15) 5=sqrt(25) 5=5 5/2 satisfies the equation 2(-3/2)=sqrt(4(-3/2)+15) -3=sqrt(9) -3=3 -3/2 does not satisfy the equation Hence, x=5/2 or 2.5

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