CALCULUS_1_(MATH_103)_3rd_trimester_2015.rtf - KENYA...

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KENYA METHODIST UNIVERSITY END OF 3 RD TRIMESTER 2015 (SB) EXAMINATION FACULTY : EDUCATION, ARTS AND SCIENCES DEPARTMENT : PURE & APPLIED SCIENCES UNIT CODE : MATH 103 UNIT TITLE : CALCULUS I TIME : 2 HOURS INSTRUCTIONS Answer any three questions Question One a. Evaluate the following limits i) lim x →∞ ( 2 x 3 + 3 x 2 5 x 1 ) (3 Marks) ii) x 0 lim ( 1 + x 2 + 2 x ) (3 Marks) iii) x 0 lim ( sin6 x 5 x ) (4 Marks) b. From the first principles, determine the derivative of (6 Marks) f(x) = x Page 1 of 4
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c. A particle moves on a straight line with velocity V = 9t 2 -20t. find an expression for the acceleration covered by the particle over the time t=3 (4 Marks) Question Two a. Find the derivatives of the following functions: (i) y = 3 x 2 x 2 + 7 (4 Marks) (ii) y = sin (4x) Inx 2 (4 Marks) b. Determine the continuity of the following function; h(x) = x 2 + 1 x 3 + 1 at x=-1 (4 Marks) c. The distance of a particle in motion at any time t is denoted and defined by s=2t 3 -4t 2 +2t Where s is in kilometers (i)
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