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Unformatted text preview: Math 1110 (Fall 2011) HW5 Presentation Problems 2 Question 1. Please solve the following two problems. (a) Find the function f ( x ) that satisﬁes f 00 ( x ) = -3 , f ( ) = 3 and f ( 2 ) = . (b) Please write the sum 7 + 1 + 7 + 2 + 7 + 3 + 7 + 4 + 7 + 5 + ··· + 7 + ( n-1 ) + 7 + n in “sigma notation” and ﬁnd a closed form expression for it. What is the value of the sum when n = 10 ? Math 1110 (Fall 2011) HW5 Presentation Problems 3 Question 2. Determine whether the following statements are (always) true or (at least sometimes) false, and circle your response. Please give a brief explanation (in complete sentences!) – a reason why it’s true, or an example where it fails. (a) The function f ( x ) = sin ( cos ( x )) + x 3 + 7 e x is integrable on the interval [ a,b ] for any real num-bers a and b . TRUE FALSE (b) The area of the region bounded by sin x and the x-axis, between x = -π and x = π is computed by Z π-π sin x dx. TRUE FALSE...
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- Harshad number, Prime number, pres, presentation problems