Suppose we are asked to evaluate the integral . If we set   and , which of the following is an expression for I in terms of u and v (NOT x)? Hints: For all real x:    For all real x:    Is the sine function even or odd?

Suppose that and   are fixed real numbers. Consider the following two limits (L and L2):    AND . Statement: The two limits are equal? (True/False)

Suppose that we are asked to find the area (A) between the curves     and    on the interval . Which of the following plots shows the shaded area between the two curves on ?

Suppose we are asked to evaluate the following integral:  . Select the appropriate choices to complete the next equivalent expressions for I:  [tanxfunc]-   [tansqfunc] .

Evaluate the following definite integral:   

Extra Credit – Bonus! Suppose the f and g are both continuous and integrable functions on . Furthermore, say that we know that for all , .  We say that the “fractional part” of x, denoted by , is the real or non-integer part of x belonging to . Also, we have that for all x. For example, , and so on. Now suppose that we want an expression for the following integral that does not involve the function f: . If we set , enter two exact (integer) expressions for the numerator and denominator of I: Numerator of I=[num]  Denominator of I=[denom]

Suppose that we want to evaluate the following integral:    Answer the following questions: Which u-sub to we choose first? u=[u] What are the corresponding lower and upper limits of integration after the u-sub? [ua] and [ub] Which of the following methods do we use to evaluate the resulting integral after the substitution (type a capital single letter)? [M2] Integration by substitution Fundamental theorem of calculus Trigonometric substitution Partial fractions Integration by parts

4.2 Name each factor of production and their compensation. (4)      

If your file is too big, upload the SECOND part here   Name accordingly:  NameSurname MATH GR9E Class T02 SBA04a – Paper 1

Instructions: Scan your answers for this test paper as ONE PDF FILE. Name your file: NameSurname MATH GR9E Class T02 SBA04a – Paper 1. Submit your PDF in one of the questions below. It is not necessary to upload the SAME PDF in all three questions.