Test3Solutions - I i i I Calculus Test#3(Chapter 4 Namt I I...

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I . I Namt - i i Calculus Test #3 (Chapter 4) ! 1. (15 pts.) I a) A student was trying to use Newton's Method to find the root of the function graphed below. No I ! matter what nonzero value the student chose for x, , he could never get the right answer. Explain, 1 using the picture beloi, why the student was never able to get an answer. *
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lb) Use Newton's Method to find the first 2 approximations (x, and x3 ) of the roots of the equation f (x) = x2 - 5, using x, = 2. Write your answer for x, rounded to 4 decimals. 2. (10 pts.) Use Calculus to find the absolute maximum and the absolute minimum values of I f(x) = x3 + 3x2 -9x + 5 on the hterval[-3,5]. : C J Z ~ ~ g'5: -3,+l ; Fcx)= x3 + 3x2 - Tk+S F'cx)= 3y= +bv-S ,x I'Q. ;P' ;x, -3 1 5
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I 3. (1 0 pts.) Sketch the graph of a single continuous function f with domain (-a, a) such that all of the I following hold simultaneously. Note that f is defined for all real numbers including x = 0. I f (x) > 0 for all x. I I , ft(x)>Oifx<O ft(x)<Oifx>O 4. (20 pts.) Evaluate the following limits .
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