Sma2161:Mathematics Ii Question Paper
Sma2161:Mathematics Ii
Course:Bachelor Of Horticulture
Institution: Meru University Of Science And Technology question papers
Exam Year:2012
QUESTION ONE (30 MARKS)
a) Evaluate the following limits i. lim???3 ??2-9 ??-3 (3 Marks) ii. lim???8 ??2-??+3 2??3+1 (3 Marks) iii. lim???0 tan ?? ?? (3 Marks) b) Find ???? ???? given that ?? = tanh 4??+1 5 . (4 Marks) c) Find ??2+5??+6 ??+2 ???? (4 Marks) d) Integrate the following by parts (4 Marks) ??2 cos?????? e) Find the values of c and d that makes f(x) continuous on the entire real number line
?? ?? =
2?? ???? ?? < 1 ????2 + ?? ???? 1 = ?? = 2 4?? ???? ?? > 2
(6 Marks)
f) Find the derivative of ?? = 3??2 + 2?? + 6 by first principles. (3 Marks)
QUESTION TWO (20 MARKS)
a) Find the derivative of the following by the rule indicated i. ?? = ?? - ?? 3 (??2 - 1) Product rule. (5 Marks)
2
ii. ?? = ??2+2 ??3-4??
Quotient rule. (5 Marks) iii. ?? = [(5?? + 2)2 + 3]4 Chain rule. (5 Marks) iv. ?? = sin?? first principles (5 Marks)
QUESTION THREE (20 MARKS)
a) Differentiate implicitly the following; i. ??2??3 - ????2 = 10???? (5 Marks) ii. ?? = sin???? (5 Marks) b) Use logarithmic differentiation to evaluate ???? ???? if i. ?? = (??2+1)9(??-3) 3 4 (??-5) 2 3(??2+2??+1) -1 3 (7 Marks)
ii. ?? = ??sin ?? (3 Marks)
QUESTION FOUR (20 MARKS)
a) Evaluate lim???8(?? - ??) (4 Marks) b) Discuss the continuity of f(x) if (4 Marks)
?? ?? =
??2-4 ??2-2
???? ?? ? 2 3 ???? ?? = 2 c) Use the definition of derivative (first principles) to find ??'(??) given that ?? ?? = 1 ??
(6 Marks) d) Find ???? ???? given ?? = ????+??-?? ????-??-?? (6 Marks)
QUESTION FIVE (20 MARKS)
a) Integrate the following by i. 6 ??2+4??-5 ???? by partial fractions. (5 Marks) ii. ?? sin?????? by parts. (4 Marks)
b) i) Sketch the curve ?? = ??3 - 3??2 + 2?? from x=0 to ?? = 3. (3 Marks) ii) Find the area included between the curve ?? = ??3 - 3??2 + 2?? and the axis for ?? = 0 to ?? = 2. (4 Marks) c) Find the volume obtained by rotating the area under the curve ?? = ?? + 1 between ?? = 1 and ?? = 2 about the ?? - ????????. (4 Marks)
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