MTH 102 Leave a Comment / By Hassan Egbetunde / July 9, 2023 Welcome to your MTH 102 Given that Sin(θ)=1/√3 and 0≤θ≤〖90〗. Find sec(θ) √3 √(3/2) 1/√3 √2 Given that Sin(θ)=1/√3 and 0≤θ≤〖90〗. Find cot(θ) √3 √(3/2) 1/√3 √2 Given that Sin(θ)=1/√3 and 0≤θ≤〖90〗. Find tan(θ) √3 √(3/2) 1/√2 √2 Given that sin(30)=1/2, and cos〖(30)=√3/2〗, obtain sin(150) 1/2 √3/2 -√3/2 -1/2 Given that sin(30)=1/2, and cos〖(30)=√3/2〗, obtain cos(210) 1/2 √3/2 -√3/2 -1/2 Given that sin45=cos45=1/√2, sin30=1/2, cos30=√3/2, calculate cos(75) √3/(2√2) (√3-1)/(2√2) (√3-1)/(2√3) (√2-1)/(2√2) Show that tan(45+A)= (1-tanA)/(1+tanA ) (A-tanA)/(A+tanA ) (1+tanA)/(1-tanA ) (tanA-1)/(1+tanA ) Find dy/dx, if y=8cos x+3sin x -8sin x+3cos x 8sin x+3cos x 3sin x+8cos x sin x+cos x Find the derivative of y=x/(x+1) (-1)/(x+1)^2 1/(x+1)^2 (x+1)^2 2/((x+1) ) If y=x^2-1/x, find dy/dx 2x-1/x^2 2x+x^2 2x-x^2 2x+1/x^2 Integrate (x^2-4x) within the limit [1,2] 11/3 3/11 -3/11 -11/3 If y=(2x+2)³,find dy/dx 3(2x+2)² 6(2x+2) 3(2x+2) 6(2x+2)² If tanθ=3/4, find the value of sinθ+cosθ 1 3/5 1 2/5 1 1/3 1 2/3 Integrate (sinx) within the range [0, π/2] 1 -1 -2 2 Integrate (2x^3+2x)/x with respect to x 2/3 x^3-2x+k x^3+2x+k 2/3 x^3+2x+k x^3-2x+k Evaluate ∫(cos4x+sin3x )dx sin4x-cos3x+k 1/4 sin4x+1/3 cos3x+k 1/4 sin4x+1/3 cos3x+k Evaluate ∫e^(x-2) dx 2e^(x-2)+c -e^(x-2)+c 1/2 e^(x-2)+c e^x+c Find dy/dx, if x^2+y^2=4 -x/y xy y/x -y/x Find dy/dx, if x+y+siny=3 (-1)/(1+siny ) (-1)/(1+cosy ) 1/(1-siny ) 1/(1+cosy ) Evaluate ∫cotx dx ln(sinx)+c In(cosx) cosx(sinx) sinx(cosx) Evaluate ∫1/x dx Inx sinx cosx tanx Evaluate ∫dx/(9+x^2 ) 1/3 arctan(x/3) 1/3 arcsin(x/3) 1/3 arccos(x/3) ln(x/3) If y=arcsinx, find dy/dx 1/√(1-x^2 ) 1/√(1+x^2 ) √(1+x^2 ) √(1-x^2 ) If y=6 sinx, find dy/dx 6cos x 6sin x 6tan x 6cotx If y=e^x (x^4), find dy/dx e^x (x^5 )(x+1) e^x (x^3) (4+x) e^x (x^5) (5+x) 3x/(x+1) Given that x³+x+y³=0, find the slope at x=1,y=1 -2 -3/2 -1/2 1/2 Integrate (1/√x-x) in the interval of [0, 1] 3/2 2 3 4 The third derivative of sin2x is? 4sin2x -4sin2x 2sin2x -4cos2x lim(x→4)[(x^3+8)/(x^2-4)] 2 3 6 -3 Find the derivative of y=a^x a^x+1 a^x lna a^x e^x lna Evaluate ∫4x/(x^2+1) dx within [0, 1] 2 8/5 In2 In4 Integrate ∫(2x-3)^3dx, within the interval [1,2] 1 -1 1/4 0 Find the derivative of In(3x+1) 1/(3x+1) e^(3x+1) 2 log(3x+1) 3/(3x+1) Given the equation of the curve x²+xy+y²=0, find its slope at the origin -2 2 -1/2 it does not exist Evaluate ∫(2x)^4dx within the interval [0,2] -101 102.4 300 14 The derivative of y=x Inx is? xInx 1+Inx 1-Inx 1+xInx lim(x→2)〖(3x^4+10)/(x^2-4)〗 48 35 24 32 Evaluate ∫4x/(x^2+3x+2) dx in the interval [0,1] 2In(3/4) 8/5 4In(9/3) In4 Differentiate the function y=√(x+1) ∛(x+1) 1/√(x+1) √1 1/√(x+1) The distance, S in meters moved by a particle in time, t in seconds is given by S(t)=3.5t^3-2t Evaluate its speed after 2 seconds 22m/s 40m/s 24m/s 28m/s Given that x=sint and y=cost, then the letter t is simply called the Time Variation Parameter Differentiate Value Considering the interval [0,k], find k given that ∫(12x^2) dx=1372. -14 14 7 8 The velocity V, in meters/sec moved by a particle in time, t in seconds is given by V(t)=12t-6t². Evaluate its distance after 2 seconds. 2m 4m 6m 8m Evaluate ∫(x^7+8) dx within the limit [1,2] 272 40 48 136 Find the position of maximum value of y if y=1-2x-x² 2,0 -1,2 2,4 0,0 Find the gradient of the curve y=x³-6x²+11x-6 at the point (1,0) -1 -2 1 2 Given f(x)=4x²-2x+(1/x), find f′(2) 13.75 8.5 -2 4 If x and y are defined by parametric equations x=2t+1 and y=3t². find dy/dx 3t (3/2)t 6t 18t The derivative of xcos3x is? -3xsin3x+cos3x -4cos3x 2sin3x -4sin2x Given that Sin(θ)=1/√3 and 0≤θ≤〖90〗. Find cosec(θ) √3 1/√3 √2 1 Time's upTime is Up!
