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InfoMAS Online Quiz for MAT 121

 

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(1) Find dy/dx if x2 - y2 = 1
[A] -x/y
[B] x/y
[C] -1/2
[D] 1/2(1 - x2)
 

(2) Find dy/dx when xy = 1

[A] -1
[B] -x-2
[C] x-2
[D] -1/x
 

(3) x2 + y2 = 2xy find dy/dx

[A] 1
[B] -1
[C] x/y
[D] -y/x
 

(4) If 2x2y = 3, find dy/dx

[A] -2y/x
[B] -2x/y
[C] -x2/y
[D] x2/y
 

(5) Let x2 + y2 + xy = 3. Find dy/dx

[A] -(2x + y)(2y + x)-1
[B]  (2y + x)(2x + y)-1
[C] - (2y + x)(2x + y)-1
[D](2x + y)(2y + x)-1 

(6) x2y2 - x - y = 0, find dy/dx

[A] - (2xy - 1)(1 - 2x2y)-1
[B] (2xy2 - 1)(1 - 2x2y)-1
[C] (1 - 2x2y)(2xy2 - 1)-1
[D](2xy - 1)(2xy2 -1)-1
 

(7) Let y = 2x3 + x2 + 1, find d2y/dx2

[A] 6x2 + 2x
[B] 2 + 12x
[C] 6x2
[D] 12x
 

(8) f(x) = (x3 - 2)(4x + 1), find d2f/dx2

[A] 16x3 + 3x2 - 8
[B]16x3 + 3x2
[C] 16x3 + 6x
[D] 48x2 + 6x
 

(9) If y = 1/x, find d3y/dx3

[A] 6x-4
[B] -6x-3
[C] -6x-4
[D] 2x-3
 

(10) y = 2x2 - 1, find d4y/dx4

[A] 4
[B] 2x
[C] 0
[D] 1
 

(11) y = (1 - 2x)2 find dy/dx
 

[A] 4(1 - 2x)
[B] -4(1 - 2x)
[C] 2(1 - 2x)
[D] -2(1 - 2x)
 

(12) y = sin 3x find dy/dx

[A] 3cos3x
[B] 3cosxsinx
[C] 3cos3xsin3x
[D]3sin3x
 

(13) y = sin32x, find dy/dx

[A] 6sin22xcos2x
[B] 6cos2x
[C] 2xcos2x
[D] 6sin2xcos22x
 

(14) If y = (sinx)c, obtain dy/dx

[A] csinxcosx
[B] c(sinx)c-1cosx
[C] c(cosx)c-1sinx
[D] ccosx
 

(15) Differentiate with respect to x, given y = sin5x

[A] 5sin4xcosx
[B] 5cosxsinx
[C] 5cos4xsinx
[D] 4sinx4cosx
 

(16) If q = sinx cosx find dy/dx

[A] sin2x - cos2x
[B] cos2x - sin2x
[C] sinx - cosx
[D] cosx - sinx
 

(17) Given that y = 2x3 - 3x2 + x, find dy/dx at x = 1

[A] 1
[B] 13
[C] -1
[D] -13
 

(18) Find the tangent to the curve y = x2 - x - 6 at x = 1/2

[A] 0
[B] -6
[C] 1/2
[D] -1/2
 

(19) Given y = log x2, find dy/dx

[A] 1/x2
[B] 2/x
[C] 2/x2
[D] 1/2x
 

(20) Given y = log(1 - x2), find dy/dx

[A] -2x(1 - x2)-1
[B] (1 - x2)-1
[C] 1 - x2
[D] 2x(1 - x2)-1
 

(21) Let v = t3 - 2t2 + t  gives the velocity of an object at time t (we define acceleration as change in velocity with time). Obtain an expression for the acceleration of the object

[A] a = 2t2 - t
[B] a = 3t2 - 4t
[C] 3t2 - 4t + 1
[D] v/t
 

(22) Find dy/dx if y = cos2x

[A] -2sin2x
[B] -2sin2xcos2x
[C] -2cos2x
[D] 2sin2x
 

(23) find dy/dx for y = cos2x

[A] -2cosx sinx
[B] -cos2x sin2x
[C] -2cosx sin2x
[D] 2sin2x cos2x
 

(24) y = sin-1(3x), find dy/dx

[A] (1 - 9x)-1/2
[B] 3(1 - 9x2)-1/2
[C] 9x2(1 + 9x2)-1/2
[D] 3(1 + 9x2)-1/2
 

(25) Find the differential coefficient of y with respect to x given that y = (3x2 - 4)4

[A] 24x(3x2 - 4)3
[B] 24x(3x2 + 4)3
[C] 24x(3x - 4)3
[D] 24x(3x2 - 4)4
 

(26) If v = sin u, d2v/du2 is what?

[A] v
[B] u
[C] -v
[D] -u
 

(27) If y = tan x, find dy/dx

[A] sin2x
[B] sec2x
[C] cos2x 
[D] cosec2x
 

(28) Given y = 2xcosx, find dy/dx

[A] 2cosx + sinx
[B] 2cosx - sinx
[C] 2(cosx + sinx)
[D] 2(cosx - sinx)
 

(29) Given that y = (1 - 2x2)-3, find dy/dx

[A] -6x(1 - 2x)2
[B] -12x(1 - 2x2)4
[C] 12x(1 - 12x2)4
[D] 12x(1 + 12x)4
 

(30) Obtain the limit of (x + 1)-1 as x--> 2

[A] 1/3
[B] 1
[C] 0
[D] 1/2
 

(31) Obtain the limit of 1/x : x-->0

[A] 1
[B] 0
[C] -1
[D] infinite
 

(32) Obtain the limit of 2(x2 - 1)-1 : x-->2

[A] 2/3
[B] 1/4
[C] 3/2 
[D] 0
 

(33) Given y = sec x, find dy/dx (Hint let = 1/cosx)

[A] tanx secx
[B] tanx cosecx
[C] cosec x
[D] -tanx secx
 

(34) Given u = cosec x, obtain du/dx

[A] -cosecx cotx
[B] tanh x
[C] cosec x cot x
[D] cosh x
 

(35) u = tan-1(3v3), obtain du/dv

[A] v2(1 + 9v2)-1
[B] v2(1 + 9v6)
[C] 9v2(1 + 9v5)-1
[D] 9v2(1 + 9v6)-1
 

(36) Find dy/dx where y = cos-1 6x

[A] -6(1 - 36x2)-1/2
[B] 6(1 - 36x2)-1/2
[C] (1 - 36x2)-1/2
[D] -1(1 - 36x2)-1/2
 

(37) If y = uvw where u, v and w are functions of x. express dv/dx

[A] (uv)dw/dx + (uw)dv/dx + (vw)du/dx
[B] (uv)dw/dx + (vw)dv/dx + (vu)du/dx
[C] (uv)dw/dx + (uw)dv/dx + (v)dwu/dx
[D] (uv)dw/dx + (uw)dv/dx - (vw)du/dx
 

(38) If y = u/v where u and v are functions of x, dy/dx is what

[A] (vu' - uv')v-2
[B] (uv' - vu')v-2
[C] (vu' - uv')2
[D] (v' - u')v-2
 

(39) If y = kx3 where (k = constant) dy2/dx2 is what?

[A] k
[B] kx2
[C] 2k
[D] 4kx
 

(40) Given that t = 5k. where k is constant, obtain dt/dk

[A] 5
[B] 0
[C]1
[D] 5k
 

(41)The limiting value of the function y(x) = 1/x as x--->3 is

[A] infinite
[B] x
[C] 0
[D] x + &
 

(42) In the neighborhood of x = -1, the function y(x) = (x3 + 1)(x + 1)-1 tends to what

[A] 3
[B] -3
[C] -1
[D] 1
 

(43) Given y(x) = sin-1ax

[A] y'(x) = a(1 - x2)-1/2
[B] y'(x) = a(1 - ax2)-1/2
[C] y'(x) = a(1 + x)-1/2
[D] y'(x) = a(1 + ax2)-1/2
 

(44) If y(x) = tan-1(x/a) then

[A] y'(x) = a(a2 + x2)-1
[B] y'(x) = a(a2 - x2)-1
[C] y'(x) = a(a2 + x2)-1/2
[D] y'(x) = a(a2 - x2)-1/2
 
 

(45) if y(x) = cosmx then

[A] yiv + m2y = 0
[B] yiv - m2y = 0
[C] yiv + m4y = 0
[D] yiv - m4y = 0
 

(46) If the function f(x) = x3 then fiv(6)  is what

[A] 24
[B] 0
[C] 6
[D] 12
 

(47) If f(x) = x4 then d3y/dx3 at x = 4 is what?

[A] 96
[B] 684
[C] 192
[D] 48
 

(48)In the  neighborhood of x = -1, the function (x4 - 1)(x - 1)-1 tends to

[A] & 
[B] 2
[C] -4 
[D] -2
 

(49) If the function y(x) = sinpx then

[A] ym = p2y
[B] ym = -p2y'
[C] ym = -p3y
[D] ym = 3p3y
 

(50) If y(x) = sinx then

[A] y' + y = 0
[B] y'' + y = 0
[C] y' - y = 0
[D] y'' - y = 0
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