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1 FINALTERM EXAMINATION Fall 9 Calculus & Aalytical Geometry-I Questio No: ( Mars: ) - Please choose oe Let f ( x) is a fuctio such that as x approaches a real umber a, either from left or right-had-side, the fuctio values icreases or decreases uboudedly the lim f ( x) x a Exist Does ot exist Questio No: ( Mars: ) - Please choose oe d(sec x) ( sec x)( ta x) ( sec x)( ta x) ( cosec x)( co t x) ( cosec x)( ta x) Questio No: ( Mars: ) - Please choose oe Cosider a fuctio h( x) ad a costat c the d (( c) { h( x)} )
2 d ( h ( x )) d ( h ( cx )) d c h( x) ( ) Questio No: 4 ( Mars: ) - Please choose oe lim f ( x) + ad lim f ( x) + If f x x + is cotiuous fuctio such that the f (, + ) has o maximum value but o miimum miimum value but o maximum both maximum ad miimum value Questio No: 5 ( Mars: ) - Please choose oe Sigma otatio is represeted by which of the followig Gree letter? χ η Σ ψ Questio No: 6 ( Mars: ) - Please choose oe I the followig figure, the area eclosed is bouded below by :
3 y x + 6 y x x x Questio No: 7 ( Mars: ) - Please choose oe y x ad y x + 6 At what poits the two curves: itersect? x ad x x ad x x ad x x ad x Questio No: 8 ( Mars: ) - Please choose oe y x ; x, x 4 Let the solid geerated by the regio eclosed betwee ad the x-axis is revolved about the y-axis. Which of the followig equatio gives the volumes of a solid by cylidrical shells? 4 V π x x 4 V x x 4 V x x 4 V x x 4 Questio No: 9 ( Mars: ) - Please choose oe
4 Let f is a smooth curve o the iterval [a, b]. What is the arc legth L of the curve f(x) defied over the iterval [a, b]? L lim + ( f '( x * )) max x L + ( f '( x * )) x lim ( '( * )) L + f x x max x L + ( f ( x * )) x Questio No: ( Mars: ) - Please choose oe For a graph to be symmetric about y-axis meas, for each poit (x,y) o the graph,the poit is also o the graph (x, -y) (-x, y) (-x, -y) Questio No: x y The graph ( Mars: ) - Please choose oe is symmetric about axis X-axis Y-axis Origi Questio No: ( Mars: ) - Please choose oe If a quatity y depeds o aother quatity x i such a way that each value of x determies exactly oe value of y, we say that y is. of x relatio
5 fuctio ot a fuctio ot a relatio Questio No: Domai of the fuctio y (, ) (, ) U + (, ) (,) ( Mars: ) - Please choose oe ( x 4) ( x ) Questio No: 4 ( Mars: ) - Please choose oe Ta(x) is cotiuous every where except at poits is π ± (,,5,...) π ± (, 4,6,...) π ± (,,, 4,5,6,...) Questio No: 5 ( Mars: ) - Please choose oe si x Lim x x Questio No: 6 ( Mars: ) - Please choose oe How the series ca be expressed i sigma otatio?
6 5 ( ) ( + ) 5 ( ) ( + ) 5 5 ( + ) ( + ) Questio No: 7 ( Mars: ) - Please choose oe y x x Let the regio bouded by the curve, the x-axis, ad the lie revolved about the y-axis to geerate a solid. Which of the followig equatio gives the volume of a solid by cylidrical shells? V x V π x V π x x V x x is Questio No: 8 ( Mars: ) - Please choose oe
7 Let y x ; x the which of the followig is the legth of the curve? d L x d L + x d L + x d L + x Questio No: 9 is ow as ( Mars: ) - Please choose oe A eve umber Irratioal Number A atural Number Ratioal Number Questio No: ( Mars: ) - Please choose oe f ( x ) for some For a fuctio f, let. f x? Does the Newto s Method wors for approximatig the solutio of ( ) Yes No Questio No: ( Mars: ) - Please choose oe
8 The Mea Value Theorem states that Let fuctio f be differetiable o (a,b) ad cotiuous o [a, b], the there exist at least oe poit c i (a,b) where. f ( b) f ( a) f '( c) b a f ( b) f ( a) f ( c) b a f ( a) f ( b) f ( c) b a f ( a) f ( b) f '( c) b a Questio No: ( Mars: ) - Please choose oe d [ F ( x )] f ( x ) If there is some fuctio F such that F( x) + C form is of f (x) the ay fuctio of the Derivative Atiderivative Slope Maximum value Questio No: ( Mars: ) - Please choose oe If f ad g are cotiues fuctio o a iterval [a, b] ad f ( x) g( x) for a x b, the area is bouded by the lies parallel to: X -axis Y-axis Both X -axis ad Y-axis Questio No: 4 ( Mars: ) - Please choose oe What is the sum of followig series?
9 ( )( + ) 6 ( + )( + ) ( + ) ( + ) Questio No: 5 ( Mars: ) - Please choose oe ( + )( + ) 4 5 ( + ) 4 5 ( + ) 4 5( + )( + ) 4 Questio No: 6 ( Mars: ) - Please choose oe If poit a is i the domai of fuctio f, the f '( x) f ( x) a a f ( x)
10 Questio No: 7 If ( Mars: ) - Please choose oe a > a > a >... > a >... { a }, the a sequece is... Icreasig Nodecreasig Decreasig Noicreasig Questio No: 8 ( Mars: ) - Please choose oe { a } For a sequece if the differece betwee successive terms sequece is ow as: a a + the the Icreasig Decreasig Nodecreasig Noicreasig Questio No: 9 ( Mars: ) - Please choose oe { a } For a sequece ow as: if the ratio of successive terms a a + < the the sequece is Icreasig Decreasig Nodecreasig Noicreasig Questio No: ( Mars: ) { a } For a sequece ow as : - Please choose oe if the ratio of successive terms a a + the the sequece is Icreasig Decreasig Nodecreasig
11 Noicreasig Questio No: ( Mars: ) - Please choose oe Which of the followig optio is true for the sequece a? Icreasig Decreasig Noicreasig Nodecreasig Questio No: ( Mars: ) - Please choose oe If the partial sum of a series is fiite the the series will/will be: Diverget Coverget Give o iformatio Questio No: ( Mars: ) - Please choose oe a + ar + ar + ar ar +... where ( a ) If the geometric series the which of the followig is true for the give series? Coverges Diverges Gives o iformatio, r < Questio No: 4 ( Mars: ) lim u + ρ + u If where be...? Coverget Diverget Give o iformatio Questio No: 5 ρ lim + u If where be...? Coverget - Please choose oe ρ > u the the series with positive terms will /will ( Mars: ) - Please choose oe ρ > u the the series with positive terms will /will
12 Diverget Give o iformatio Questio No: 6 ( Mars: ) - Please choose oe I alteratig series test, which oe of the followig coditio must be satisfied? lim a a > a > a... > a >... a a a... a... Questio No: 7 ( Mars: ) - Please choose oe ( ) a A series of the form is called. Alteratig series Geometric series Arithmetic series Harmoic series Questio No: 8 ( Mars: ) - Please choose oe x Which of the followig is the Maclauri series for e? x x x + x !!! x x x x !!! x x + x !! x x x !!
13 Questio No: 9 ( Mars: ) - Please choose oe Which of the followig is the wor doe W if a object moves i the positive directio alog a coordiate lie while subject to a force F(x) i the directio of motio over a iterval [,]? W W W W x x F( x) F( x) Questio No: 4 ( Mars: ) - Please choose oe Which of the followig is the sprig costat if a sprig whose atural legth is m exerts a force of N whe stretched m beyod its atural legth? x N/m m m/n Questio No: 4 ( Mars: ) Evaluate the followig itegral by substitutio method. x (x + ) Questio No: 4 ( Mars: ) Fid the limits of the itegral idicatig the area bouded by the y x ad y x + 6 curves. Sol,
14 Questio No: 4 ( Mars: ) What will be the amout of wor doe if a object moves 7m i the directio of a force of 7N? Questio No: 44 ( Mars: ) Evaluate the followig itegral: 5 6si x si x Questio No: 45 ( Mars: ) Fid a defiite itegral idicatig the area of the surface geerated by revolvig y x ; y 4 the curve about the x axis. But do ot evaluate the itegral. Questio No: 46 ( Mars: ) Fid the sprig costat ; if a force of N is required to stretch a sprig from its atural legth of 4.8m to a legth of 6.8m? Questio No: 47 ( Mars: 5 ) d [ f ( x) ] x 6x + Let. Fid f ( x) Sol, Questio No: 48 ( Mars: 5 ) Use the cylidrical shell to fid the volume of the solid geerated whe the y x, x, y regio eclosed by the curve is revolved about the y-axis. Questio No: 49 ( Mars: 5 ) { a } Determie whether the sequece coverges or diverges; if it coverges the fid its limit; 4 + a 4 where Questio No: 5 ( Mars: )
15 Fid the area of the regio that is eclosed by the curves y x ad y x betwee x ad x 4.
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