Symbolic answers must be entered using notation similar to the examples given below. If you enter decimal numbers for questions that indicate that a symbolic answer is required, it will be marked as zero, regardless of whether the decimal number is correct or not. Integer numbers (positive, negative, and O) are allowed. Below are some examples. Example Math Expression How to Enter the Answer 2 -3/5 infinity 2\"8+l 2+exp(5) 5*pi/9 4/7-3*ln (2) sqrt(2) 5"(l/3) sqrt(5exp(3)+2*ln(7*pi)) fac(5) Problem # 3: A rectangular plot of land is to be enclosed by a fence. Furthermore an additional section of fence is set parallel to one side, cutting the plot into two smaller rectangles. If 240 meters of fence are available, what is the greatest area of land that can be fenced in this manner? l Just Save l l Submit Problem #3 for Grading Problem #3 Attempt #1 Attempt #2 Attempt #3 Your Answer: 60 240 Your Mark: 0/2x 0/2X Answer Format Unless otherwise noted, enter answers as: - Whole Numbers - Exact Fractions (e.g., 2/3 or -5/4) or (only when necessary): - Decimals correct to six decimal places The use of decimal numbers is discouraged because decimal numbers are subject to rounding errors, which could cost you marks! Sections 5.1-5.4 in the textbook. PI'Oblem # 1: Estimate the area under the graph of f (x) = 2 + x2 on the interval [1, 5] using, (a) Six rectangles and left endpoints. (b) Three rectangles and left endpoints. Problem #2: Find an expression for the area under the graph of f(x) =,,2 +8 on the interval [1, 2]. n 1+2 n 1 + 2i 1 + 2i (A) lim (B) lim (C) lim n SIN I'M n ->oo i=1 Ling ( 1 + i ) 2 + 8 ( 1 + 2 ) i= 1 9 ( 1 + 21 ) 2 + 8 ( 1 + 2i ) 9 ( 1 + 2i ) 2 + 8 n 1+1 1 + 2i (D) lim n (E) lim I'MS SIN (F) lim SIN 00+ 1 n 9( 1 +2)- +8 00 + U 9 ( 21 ) -+8 9 ( 1 + ( 21 ) - ) + 8 n 1+i (G) lim n S IN n 9( 1 + ( 2 ) - ) + 8 (H) lim 00 + u 1= 1 9 ( 2 ) - + 8 Problem #2: Select v Just Save Submit Problem #2 for Grading Problem #2 Attempt # 1 Attempt #2 Attempt # 3 Your Answer: Your Mark: Problem #3: The graph of f is given to the right. Evaluate N y Ff (x ) 3 -2 -1 0 1 2 -1 X -2 Enter your answer symbolically, Problem #3: as in these examplesProblem #4: Evaluate the following integrals by interpreting them in terms of areas. (2) [1x - 51 dx (b) Enter your answer symbolically, Problem #4(a): as in these examples Enter your answer symbolically, Problem #4(b): as in these examples Just Save Submit Problem #4 for Grading Problem #4 Attempt # 1 Attempt #2 Attempt # 3 Your Answer: |4(a) 4(a) 4(a) 4(b) 4(b) 4(b ) Your Mark: | 4(a) 4(a) 4 (a ) 4 (b ) 4 (b ) 4 ( b ) Problem #5: The graph of f is given to the right. N *=f (x) 1 3 -2 O 2 X -2 (a) Find g(1). (b) Find g'(1). (c) Find g"(-2). (d) On what interval is g decreasing? Enter your answer symbolically, Problem #5(a): as in these examples Problem #5(b): Problem #5(c): Problem #5(d): If your interval is (a,b) then enter a,b in the answer box.Problem #6: Evaluate the following integrals. (a) V 3/2 6 VI - dx Problem #6(a): Enter your answer symbolically, as in these examples Problem #6(b): Enter your answer symbolically, as in these examples Just Save Submit Problem #6 for Grading Problem #6 Attempt # 1 Attempt #2 Attempt # 3 Your Answer: | 6(a) 6(a) 6(a) 6(b) 6 (b ) 6 (b ) Your Mark: |6(a) 6(a) 6(a) 6(b) 6 (b ) 6 (b ) Problem #7: Let F(x) = [*~ Vi+ dt. Find F'(3). Problem #7: Enter your answer symbolically, as in these examples Just Save Submit Problem #7 for Grading