MATH 102 [Homework 1: Due on Monday, Feb. 21]
Instructions:
1. Please write the statement of the problem and then solve the question.
2. Solution must be written neatly explaining all the steps.
3. Staple your sheets before giving to the instructor.
4. Fold your homework papers and write your Serial #, and Section # on the top of the cover page.
1. [Use Calculator and find answer up to 3 decimal places] Approximate the area under the curve
y  x3  esin x  2cosh x on the interval [–8,9] by using 2, 4, 7 rectangles of equal width with height
as mid-point of the base of the interval of the rectangles.
2. Find the antiderivative of the following functions:
7
7
3
x
i) 5m 9  cot 2 m ii)

iii) ( x  7) 6  cos 2
2
4 z 5(1  z )
2
dy
2
2

 x  3 ; y ( )  4
3. Find the solution of the Differential Equation:
dx csc x
 3

3
1
4. Evaluate: i)  

dt ii)  5w  7 cot w csc w dw iii) 
dx

2
2
1

cos
2
x
1

t
2
t
t

1


5. Suppose that a point moves along some unknown curve y = f (x) in the xy-plane in such a way that at
each point (x,y) on the curve, the tangent line has the slope 1  tan 2 x . Find an equation of the curve
 
given that it passes through the point  5,  . [You must read Example 6 at page 383 of the text
 4
before solving this question]
3
6. a) Sketch the graph of y  2 x  1  by drawing proper xy-plane, and using shifts and appropriate
2
measurements on the axes.
b) Using the graph in (a), find the area function A(x) under the graph in the interval [-4, x].
c) Find the Derivative of the Area Function.
d. Is A(x) differentiable for all values of x.? Explain.

