Test 1 Sample
1
Engineering Mathematics 1 B.A. Mahad TEST 1 SSCE 1693 Page 1 TEST 1 Instruction: Answer All Questions 1. Using the appropriate identities or other method to show that a) x h x x 2 sec tanh 1 tanh 1 2 2 (3 marks) b) x x 2 cosh 1 cosh 2 2 (3 marks) 2. Solve the following for x, giving your answer in 4 decimal places 1 sinh 2 cosh x x (4 marks) 3. Find the derivative of a) x x y sec 1 tanh 1 (3 marks) b) x x y 4 cosh 4 cos 1 (3 marks) c) ) 3 (tan sinh 1 x y (3 marks) 4. Use appropriate substitution to solve dx e x x x 2 sin 2 cos (4 marks) 5. Use tabular method to solve xdx e x 2 cos 3 (4 marks) 6. Use partial fraction to solve dx x x x 2 3 2 3 2 (4 marks) 7. Solve the following integrals a) xdx h x 2 sec tanh (3 marks) b) dx x e x 2 sin 1 1 (3 marks) c) 3 2 2 x x dx (3 marks)
Transcript of Test 1 Sample
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Engineering Mathematics 1 B.A. Mahad TEST 1
SSCE 1693 Page 1
TEST 1 Instruction: Answer All Questions
1. Using the appropriate identities or other method to show that
a) xhxx 2sec
tanh1tanh1
2
2
(3 marks)
b) xx 2cosh1cosh2 2 (3 marks)
2. Solve the following for x, giving your answer in 4 decimal places
1sinh2cosh xx (4 marks)
3. Find the derivative of
a) xxy
sec1tanh 1
(3 marks)
b) xxy 4cosh4cos 1 (3 marks)
c) )3(tansinh 1 xy (3 marks)
4. Use appropriate substitution to solve dxexx x
2sin2cos (4 marks)
5. Use tabular method to solve xdxe x 2cos3 (4 marks)
6. Use partial fraction to solve dxxx
x23
232 (4 marks)
7. Solve the following integrals
a) xdxhx 2sectanh (3 marks)
b) dxx
e x
2
sin
1
1
(3 marks)
c) 322 xx
dx (3 marks)
