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<=KNEC Diploma in Electrical and Electronics Engineering(Power option, Telecommunication Option, Instrumentation Option)Engineering Mathematics I Module 1 past paper: November 2016

Evaluate the integrals:

$int sin^2 3x dx$

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Questions List:

1. Solve the equation

$sqrt(x)=frac{3+x}{sqrt(12)}$

2. Solve the equation:

$3^(x^2 )$ =

$27^(x+1)$ correct to two decimal places

3. The cost of 5 resistors, 4 capacitors and 1 diode is Ksh 340; the cost of 10 resistors, 9 capacitors and 4 diodes is Ksh 880; while the cost of 10 resistors, 13 capacitors and 15 diodes is Ksh 1920. Use elimination method to determine the cost of each component.

4. Use the binomial theorem to expand

$((1-2x)/(1+3x))^(1/3)$ up to term in

$x^2$ .

5. Given the complex numbers

$Z_2$ =3+j, determine

$Z_1/Z_2$ , expressing the answer in exponential form.

6. Solve the equation

$log⁡(x^2+6)-logx=log5.$

7. Solve the equation

$4Cos2theta-2Sintheta+2=0$ for

$0^0≤theta≤360^0.$

8. The longest side of a right angled triangle is (x+9)cm. if the length of the other remaining sides are (x+5)cm and (2x+6)cm, determine the; i)dimensions of the triangle; ii)area of the triangle.

9. Prove the hyperbolic identities:

$tanh(theta-phi)=(tanhtheta-tanhphi)/(1-tanhthetatanhphi)$

10. evaluate the integrals:

$int (3x-5)^4 dx$

11. Evaluate the integrals:

$int sin^2 3x dx$

12. Evaluate the integrals:

$int _6^7 (18+21x-x^2)/((x-5)(x+2)^2)dx$

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