1) 2) 3) Use the definition to find an expression for the instantaneous acceleration of an object moving with rectilinear motion according to the given function. The instantaneous acceleration is defined as the instantaneous rate of change of the velocity with respect to time. The displacement (s) as a function of time (t) is given below. Find the velocity as a function of t, and then find the acceleration. 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 1) 8 y x 3 x 2 2 x 7 3 y 3 x 2 y 6 x y 4 6 y 5 0 16 x2 3 16 3 2) 3) Use the definition to find an expression for the instantaneous acceleration of an object moving with rectilinear motion according to the given function. The instantaneous acceleration is defined as the instantaneous rate of change of the velocity with respect to time. The displacement (s) as a function of time (t) is given below. Find the velocity as a function of t, and then find the acceleration. Correct option is C 4) The equation of tangent line is Correct graph is B 5) y 1 8x The equation of normal line is x 4 y 5 5 Correct graph is B 6) Relative maxima A. 2, 29 Relative minima A. 2, 35 Point of inflection A. 0, 3 Correct graph is A 7) Correct graph is B 8) Correct graph is D 9) Length and width both should be 12, enter answer as 12,12 10) dy x x 16 cot 3 csc 2 dx 2 2 11) 88 cm/s 12) 13) 14) , here ln is natural log with base e 40 x ln10 15) Correct option is A 16) The derivative is 17) a) The value of function f, when x approaches \"a\" from the left, known as left hand limit of f(x) at x=a b) The value of function f, when x approaches \"a\" from the right. known as right hand limit of f(x) at x=a c) Here lim x->0+ (2^(1/x)) is equals to \"infinity\". However lim x->0- (2^(1/x)) is equals to \"zero\". Since both are not same, the given statement is TRUE d) The value of the function f, near x=0(not at exactly x=0) 18) 3 e2 x A.lim x 2 ln x 19) , answer is infinity. x 4 x C 4 20) 6 z 5 10 z C 21) 10 tan 3 x C 3 22) No, if we use the substitution u=x^2-1, then we will have du=2xdx and hence we need to integrate (u^2)*sqrt(u+1) which will become more complicated. In this case it is better to expand (x^2-1)^2 as x^42x^2+1 and then use power rule to integrate. 23) because 1 A.No x 10 dx x 9 C 9 24) 10 plus 1 is 9 i 0.1t 5 5t 2 7 1) 8 y x3 x 2 2 x 7 3 y 3 x 2 y 6 x y 6 4 y 5 0 16 x2 3 16 3 2) 3) Use the definition to find an expression for the instantaneous acceleration of an object moving with rectilinear motion according to the given function. The instantaneous acceleration is defined as the instantaneous rate of change of the velocity with respect to time. The displacement (s) as a function of time (t) is given below. Find the velocity as a function of t, and then find the acceleration. Correct option is C 4) The equation of tangent line is y 1 8 x Correct graph is B 5) The equation of normal line is y Correct graph is B x 4 5 5 6) Relative maxima A. 2, 29 Relative minima A. 2, 35 Point of inflection A. 0, 3 Correct graph is A 7) Correct graph is B 8) Correct graph is D 9) Length and width both should be 12, enter answer as 12,12 10) dy x x 16cot 3 csc2 dx 2 2 11) 88 cm/s 12) 13) 14) 40 , here ln is natural log with base e x ln10 15) Correct option is A 16) The derivative is 17) a) The value of function f, when x approaches \"a\" from the left, known as left hand limit of f(x) at x=a b) The value of function f, when x approaches \"a\" from the right. known as right hand limit of f(x) at x=a c) Here lim x->0+ (2^(1/x)) is equals to \"infinity\". However lim x->0- (2^(1/x)) is equals to \"zero\". Since both are not same, the given statement is TRUE d) The value of the function f, near x=0(not at exactly x=0) 18) 3 e2 x , answer is infinity. x 2 ln x A.lim 19) 4 x x C 4 20) 6 z 5 10 z C 21) 10 tan 3 x C 3 22) No, if we use the substitution u=x^2-1, then we will have du=2xdx and hence we need to integrate (u^2)*sqrt(u+1) which will become more complicated. In this case it is better to expand (x^2-1)^2 as x^4-2x^2+1 and then use power rule to integrate. 23) 1 A.No x 10 dx x 9 C because 10 plus 1 is 9 24) 9 i 0.1t 5 5t 2 7