Differentiation
Derive the product rule for the differentiation of the product of three differentiable functions, that is , d/dx(f(x)g(x)h(x)). Thank You!
Derive the product rule for the differentiation of the product of three differentiable functions, that is , d/dx(f(x)g(x)h(x)). Thank You!
A curve has the equation y= (x-a)√(x-b) for x≥b, where a and b are constants. It intersects the x-axis at the point A with x=b+1. Show that the gradient of the curve of A is 1. Thank...
Given that y= x√(3-x2) , show that dy/dx = (3+2x2) / (√3+x2 ) . Is it possible to get a positive x value? My answer is (3-2x2) / √(3-x2 ) . Thank...
Given that y= (x2+1)n, where n is a positive integer, show that the ratio of dy/dx when x =1 to d2y/dx2 =1:n. Thank you!
Given that y= 1/√(x2 +3), show that (x2 +3) dy/dx +xy =0 Thank You!
Show that 2 tan20° + 4 tan40° + 8 tan 80° = 9(cot10° - tan10°). Thank you :)
Given that cotθ=k and that θ is acute, express tan3θ in terms of k. Ans: (3k2-1)/(k)(k2-3) Thank you :)
(i) Given that cos A =3/5 and cos(A+B) =-5/13, where A and B are acute, evaluate sin B. (ii) Another acute angle C is such that sin C=12/13. Find sin(A+B+C). (iii)...
A and B are acute angles such that sin(A-B)=1/2 and sin A cos B= 7/10. Without using a calculator, find the value of tanA/tanB. Ans: 7/2 Thank...
(i) Prove that cos ( A+B+C) = cos A cos B cos C- sin A sin B cos C -sin A. (ii) Hence show that cos 3A= 4 cos3A- 3 cos A. Thank...
Solve each of the following equations. (i) 3cos2 2x+ 4 sin2x =1 , 0° < x < 360° (ii) sec x (tan x -2) = 2 cosec x , 0° < x < 360° (iii)...
If 2tan2θ = 5 secθ+ 10, where θ is obtuse, find the value of tan θ without the use of calculator. Ans: -√5/2 Thank you :)
Given that log2x=p and log4y=q, express x2y in terms of p and of q. Ans: 22p+2q Thank You :)
Solve for x and y, the simultaneous equations 4x+3 =32(2x+y ) and 9x + 3y =1o Ans: x=0.631 and y=1.631 Thank you :)
Express each of the following in the form in x=ax + b, and find the value of a and of b. (i) xe-x =2.46 (ii) (xex)2 = 30e-x Ans:(i) a=1,...
If 2 logax= 1+loga(7x-10a), find x in terms of a. Ans: 2a, 5a
(i) Factorize the expression 2 sin x cos x - cos x + 4 sin x -2. (ii) Hence solve the equation 2 sin x cos x - 2=cos x - 4 sin x for -360°≤ x ≤ 360°
Solve for 0°<x<180° for the following equation, 8 cosec 2x cot 2x=3
Given that a>b>1 and that 2 logab + 4 logba=9, find b in terms of a. Ans: b=√a
(i) Solve the equation log2(x3+1) - 2 log2x = log2(x2-x+1) -2 (ii) Hence solve the equation log2(x3+1) - log2x2 =log2(x2-x+1)-2 Ans: (i) 2+2√2 ...