Calculus/Calculus I/Calculus II BS 1 Semester/Term University Of Sargodha (UOS) 2022
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University of Sargodha
30226
Sabiest: CATSE
BS. 1" Term Examination 2022
Time Allowed: 02:30 Hours
Laper: Calculus& danical Geometr: (MATH-3213/MATH-1011
Maximam Marko: 60
Note: Objective part is compulsory. Attempt any three questions from subjective part.
Objective Part (Compulsory)
(2*12)
Q.1.
Write short answers of the following in 2-3 lines cach on your answer sheet.
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• Then Evaluate /Q,-1,6)
IF (0) = 2 costi+sin i + 2ik, then find
Is y sand s are continuous at 9s Ech prove thar fe is also continuous at "a".
For which Functions, we can galeuinte lim / (x) by simply calculating / (Xo)
Define horizontal asymptote. Give an example.
Define curvature.
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Find lim (P.d. -2cosm).
Find domain of function =(t) - cosmi - Intj+J-2k
Define orthogonal projections of vectors.
Give precise definition of
(6) lim /(x) =5
(i) lim /(x) =5
What is the average rate of change of the function sto over the interval from tra to t-b? How is it
related to a secant line?
Q.2.
c+2
Subjective Part
(3*12)
IS-1
, find c so that lim / (x) exists
0.3.
(k) Find the area of surface generated by revolving a curve y = 2Vx, 15x S2 about the x-axis.
(b) Find y" by implicit differentiation x" + 4y' = 4
Q.4.
(a) Solve the initial value problem.
dy = 6, y°(0) = - 8, Y(0) = 0, y(0) = 5
(b) Graph the parabola y = 2x' -x+3. Label the vertex, axis, and intercepts.
(1) Given a continuous function y = x (4 - x).
Find the intervals on which / Is increasing and the intervals where / is decreasing.
Find where the graph of is concave up and where it is concave down
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0.6.
(b) Show that lim
- L.K-6049
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