Questions and Answers of Financial Accounting Information For Decisions

a. Differentiate (3x2 – 1)5 with respect to x.b. Hence finds fx( 3x² - 1)* dx.
Evaluate.a.b.c.d.e.f. (2x + 1)° dx
a. Given that y = x√3x2 + 4, find dy/dx.b. Hence evaluates 3x? dx. V3x? + 4 0.
Find the area of each shaded region.a.b.c.d. ソラx(x-2)
Find y in terms of x for each of the following.a. dy/dx = 7x6 + 2x4 + 3b. dy/dx = 2x5 – 3x3 + 5xc. dy/dx = 3/x4 – 15/x2 + xd. dy/dx = 18/x10 + 6/x7 -2
Find the area of the region bounded by the curve y = 2 + 3x – x2, the line x = 2 and the line y = 2. y= 2+3x- x?
Find each of the following.a.b.c.d.e.f. (x + 2)(x + 5) dx
A curve is such that dy/dx = (4x + 1)4.Given that the curve passes through the point (0, - 1.95) find the equation of the curve.
Find:a.b.c.d.e.f. Je* (5 - e*) dx
Finda.b.c.d.e.f. (1- sin x) dx
A curve is such that dy/dx = 5/2x – 1 for x > 0.5.Given that the curve passes through the point (1, 3), find the equation of the curve.
a. Find ʃ(1 – 6/x2) dx.b. Hence find the value of the positive constant k for which 3k dx = 2.
a. Differentiate x ln x with respect to x.b. hence finds ʃ ln x dx.
Evaluate.a.b.c.d.e.f.g.h.i. e2x dx 0.
a. Given that y = 1/x2 + 5, find dy/dx.b. Hence evaluates 4x dx. (x² + 5 )*
Find the total shaded region.1. у%3 (x+2)(х+ 1) (х-1) -2 -1
Find y in terms of x for each of the following.a. dy/dx = 3x(x – 2)b. dy/dx = x2(4x2 – 3)c. dy/dx = (x + 2√x)2d. dy/dx = x(x – 3) (x + 4)e. dy/dx = x5 – 3x/2x3f. dy/dx = (2x – 3) (x –
Find the area of the region bounded by the curve y = 3x2 + 2, the line y = 14 and the y-axis. y = 3x2 + 2 %3D 14 Ol
Find each of the following.a.b.c.d.e.f. x2 - 5 dx .2
A curve is such that dy/dx = √2x + 1.Given that the curve passes through the point (4, 11) find the equation of the curve.
Find:a.b.c. 2e* + dx
A curve is such that dy/dx = cos x – sin x.Given that the curve passes through the point (π/2, 3), find the equation of the curve.
A curve is such that dy/dx = 2x + 5/x for x > 0.Given that the curve passes through the point (e, e2), find the equation of the curve.
The diagram shows part of the curve of y = 9x2 – x3, which meets the x-axis at the origin O and the point A. The line y – 2x + 18 = 0 passes through A and meets the y-axis at the point B.a. Show
a. Show that d/dx(ln x/x) = 1 – ln x/x2.b. Hence finds Inx dx.
Evaluate.a.b.c.d.e.f. | sin x dx
A curve is such that dy/dx = 3x2 – 4x + 1.Given that the curve passes through the point (0, 5) find the equation of the curve.
Find the area of the shaded region.1. y 2 sin 2x +3 cos x RIN
A curve is such that dy/dx = 1/√10-x.Given that the curve passes through the point (6, 1), find the equation of the curve.
A curve is such that dy/dx = 2e2x + e-x.Given that the curve passes through the point (0, 4), find the equation of the curve.
A curve is such that dy/dx = 1 – 4 cos 2x.Given that the curve passes through the point (π/4, 1), find the equation of the curve.
A curve is such that dy/dx = 1/x+e for x > -e.Given that the curve passes through the point (e, 2 + ln 2), find the equation of the curve.
The diagram shows part of the curve y = 2 sin 3x. The normal to the curve y = 2 sin 3x at the point where x = π/9 meets the y-axis at the point P.a. Find the coordinates of P.b. Find the area of the
a. Given that y = x√x2 – 4, find dy/dx.b. Hence finds x2 – 2 dx. Vx² - 4 .2
Evaluate.a.b.c.d.e.f. 2 dx 1 3x +1
a. Show that d/dx (x/cos x) = cos x + x sin x/cos2 x.b. Hence evaluate. 4 COS x + x sin x dx. 5 cos? x
Find the area enclosed by the curve y = 6/√x, the x-axis and the lines x = 4 and x = 9.
A curve is such that dy/dx = 6x(x – 1).Given that the curve passes through the point (1, - 5) find the equation of the curve.
The diagram shows an isosceles triangle PQR inscribed in a circle, centre O, radius r cm.PR = QR and angle ORP = θ radians.Triangle PQR has an area of A cm2.a. Show that A = r2 sin 2θ + r2 sin 2θ
The diagram shows a semi-circle with diameter EF of length 12 cm.Angle GEF = θ radians and the shaded region has an area of A cm2.a. Show that A = 36θ + 18 sin 2θ.b. Given that θ is increasing at
A curve has equation y = x2ex.The curve has a minimum point at P and a maximum point at Q.a. Find the coordinates of P and the coordinates of Q.b. The tangent to the curve at the point A(1, e) meets
A curve has equation y = x ln x.The curve crosses the x-axis at the point A and has a minimum point at B.Find the coordinates of A and the coordinates of B.
A curve has equation y = Ae2x + Be-2x.The gradient of the tangent at the point (0, 10) is – 12.a. Find the value of A and the value of B.b. Find the coordinates of the turning point on the curve
The diagram shows a circle, centre O, radius r cm. The points A and B lie on circle such that angle AOB = 2θ radians.i. Find, in terms of r and θ, an expression for the length of the chord AB.ii.
Find the coordinates of the stationary points on these curves and determine their nature.a. y = 4 sin x + 3 cos x for 0 ≤ x ≤ π/2b. y = 6 cos x/2 + 8 sin x/2 for 0 ≤ x ≤ 2πc. y = 5 sin
A curve has equation y = x/x2 + 1.i. Find the coordinates of the stationary points on the curve.ii. Show that d2y/dx2 = px3 + qx/(x2 + 1)3, where p and q are integers to be found, and determine the
Find the coordinates of the stationary points on these curves and determine their nature.a. y = xex/2b. y = x2e2xc. y = ex – 7x + 2d. y = 5e2x – 10x – 1e. y = (x2 – 8)e-xf. y = x2 ln xg. y =
Variables x and y are such that y = (x -3) ln(2x2 + 1).i. Find the value of dy/dx when x = 2.ii. Hence find the approximate change in y when x changes from 2 to 2.03.
A curve has equation y = ln(x2 – 2)/x2 – 2.Find the approximate change in y as x increases from √3 to √3 + p, where p is small.
The point A, where x = 0, lies on the curve y = ln(4x2 + 3)/x-1. The normal to the curve at A meets the x-axis at the point B.i. Find the equation of this normal.ii. Find the area of the triangle
Variables x and y are connected by the equation y = 3 + 2x – 5e-x.Find the approximate change in y as x increases from ln 2 to ln 2 + p, where p is small.
A curve has equation y = A sin x + B cos 2x.The curve has a gradient of 5√3 when x = (π/6) and has a gradient of 6 + 2/√2 when x = π/4.Find the value of A and the value of B.
i. Given that y = tan 2x/x, find dy/dx.ii. Hence find the equation of the normal to the curve y = tan2x/x at the point where x = π/8.
Variables x and y are connected by the equation y = ln x/x2 + 3.Find the approximate change in y as x increases from 1 to 1 + p, where p is small.
A curve has equation y = A sin x + B sin 2x.The curve passes through the point P(π/2, 3) and has a gradient of 3√2/2 when x = π/4.Find the value of A and the value of B.
A curve has equation y = 2x sin x + π/3. The curve passes through the point P(π/2, a).a. Find, in terms of π, the value of a.b. Using your value of a, find the equation of the normal to the curve
Variables x and y are connected by the equation y = 3 + ln(2x – 5)Find the approximate change in y as x increases from 4 to 4 + p, where p is small.
Find dy/dx for each of the following.a. ey = sin 3xb. ey = 3 cos 2x
A curve has equation x = ½ [ey(3x + 7) + 1].Find the value of dy/dx when x = 1.
The diagram shows part of the curve y = ln(x + 1) – ln x. The tangent to the curve at the point P(1, ln 2) meets the x-axis at A and the y-axis at B. The normal to the curve at P meets the x-axis
Variables x and y are connected by the equation y = sin 2x.Find the approximate increase in y as x increases from π/8 to π/8 + p, where p is small.
a. By writing sec x as 1/cos x, find d/dx(sec x).b. By writing cosec x as a/sin x, find d/dx (cosec x).c. By writing cot x as cos x/sin x, find d/dx(cot x).
Find dy/dx for each of the following.a. ey = 4x2 – 1b. ey = 5x3 – 2xc. ey = (x + 3) (x – 4)
Variables x and y are such that y = e2x + e-2x.a. Find dy/dx.b. By using the substitution u = e2x, find the value of y when dy/dx = 3.c. Given that x is decreasing at the rate of 0.5 units s-1, find
A curve has equation y = x ex.The tangent to the curve at the point P(1. e) meets the y-axis at the point A.The normal to the curve at P meets the x-axis at the point B.Find the area of triangle OAB,
Find the gradient of the tangent toa. y = 2x cos 3x when x = π/3b. y = 2 – cos x/3 tan x when x = π/4.
Find dy/dx for each of the following.a. y = log3 xb. y = log2 x2c. y = log4 (5x – 1)
A curve has equation y = xex.a. Find, in terms of e, the coordinates of the stationary point on this curve and determine its nature.b. Find, in terms of e, the equation of the normal to the curve at
Given that y = x2/cos 4x, finda. dy/dx,b. The approximate change in y when x increases from π/4 to π/4 + p, where p is small.
A curve has equation y = 5 – e2x.The curve crosses the x-axis at A and the y-axis at B.a. Find the coordinates of A and B.b. The normal to the curve at B meets the x-axis at the point C.Find the
Differentiate with respect to x.a. ecos xb. ecos 5xc. etan xd. e(sin x + cos x)e. ex sin xf. ex cos1/2xg. ex(cos x + sin x)h. x2ecos xi. ln(sin x)j. x2 ln(cos x)k. sin 3x/e2x-1l. x sin x/ex
Use the laws logarithms to help differentiate these expressions with respect to x.a.b. ln 1/(2x - 5)c. ln[x(x - 5)4]d. ln(2x + 1/x -1)e. ln(2 - x/x2)f. ln [x(x + 1)/x + 2]g. ln [2x + 3/(x-5)(x+1)]h.
A curve has equation y = 5e2x – 4x – 3.The tangent to the curve at the point (0, 2) meets the x-axis at the point A. Find the coordinates of A.
A curve has equation y = e1/2x + 1.The curve crosses the y-axis at P.The normal to the curve at P meets the x-axis at Q.Find the coordinates of Q.
Variable x and y related by the equation y = 10 – 4 sin2 x, where 0 ≤ x ≤ π/2.Given that x is increasing at a rate of 0.2 radians per second, find the corresponding rate of change of y when y
A curve has equation y = x sin 2x for 0 ≤ x ≤ π radians.a. Find the equation of the normal to the curve at the point P(π/4, π/4).b. The normal at P intersects the x-axis at Q and the y-axis at
Differentiate with respect to x.a. x sin xb. 2 sin 2x cos 3xc. x2 tan xd. x tan3 (x/2)e. 5/cos 3xf. x/cos xg. tan x/xh. sin x/2 + cos xi. sin x/3x – 1j. 1/sin3 2xk. 3x/sin 2xl. sin x + cos x/ sin x
A curve has equation y = x2 ln 3x.Find the value of dy/dx and d2y/dx2 at the point where x = 2.
Find the equation of the tangent toa. y = 5/e2x + 3 at x = 0b.c. y = x2(1 + ex) at x = 1. y = Ve2* +1 at x = In 5 %3D
Find dy/dx whena. y = cos 2x sin (x/3),b. y = tan x/1 + ln x.
Differentiate with respect to x.a. sin3 xb. 5 cox2 (3x)c. sin2 x – 2 cos xd. (3 – cos x)4e. 2 sin3(2x + π/6)f. 3 cos4 x + 2 tan2(2x – π/4)
Differentiate with respect to x.a. x ln xb. 2x2 ln xc. (x – 1) ln xd. 5x ln x2e. x2 ln (ln x)f. ln 2x/xg. 4/ ln xh. ln(2x + 1)/x2i. ln(x3 – 1)/2x + 3
Differentiate with respect to x.a. xexb. x2e2xc. 3xe-xd. √x exe. ex/xf. e2x/√xg. ex+1/ex-1h. xe2x – e2x/2i. x2ex – 5/ex + 1
a. Find the equation of the tangent to the curve y = x3 – ln x at the point on the curve where x = 1.b. Show that the tangent bisects the line joining the points (-2, 16) and (12, 2).
A curve has equation y = 3 sin (2x + π/2).Find the equation of the normal to the curve at the point on the curve where x = π/4.
Differentiate with respect to x.a. 2 + sin xb. 2 sin x + 3 cos xc. 2 cos x – tan xd. 3 sin 2xe. 4 tan 5xf. 2 cos 3x – sin 2xg. tan(3x + 2)h. sin(2x + π/3)i. 2 cos(3x – π/6)
Differentiate with respect to x.a. ln 5xb. ln 12xc. ln (2x + 3)d. 2 + in(I – x2)e. ln(3x + 1)2f. ln √x + 2g. ln(2 – 5x)4h. 2x + ln(4/x)i. 5 – ln 3/(2 – 3x)j. ln (ln x)k. ln (√x + 1)2l.
Differentiate with respect to x.a. e7xb. e3xc. 3e5xd. 2e-4xe. 6e-x/2f. e3x+1g, ex2+1h. 5x – 3e√xi. 2 + 1/e3xj. 2(3 – e2x)k. ex + e-x/2l. 5(x2 + ex2)
Relative to an origin O, the position vectors of points P, Q and R are -6i + 8j, -4i + 2j and 5i + 5j respectively.a. Find the magnitude of:i. PQ(vector)ii. PR(vector)iii. QR(vector).b. Show that
Relative to an origin O, the position vector of P is 8i + 3j and the position vector of Q is – 12i – 7j. R lies on the x-axis and OR(vector) = OP(vector) + µOQ(vector).Find OR(vector).
Relative to an origin O, the position vector of A is -6i + 4j and the position vector of B is 18i + 6j. C lies on the y-axis and OC(vector) = OA(vector) + λOB(vector). Find OC(vector).
Relative to an origin O, the position vectors of A, B and C are -2i + 7j, 2i – j and 6i + λj respectively.a. Find the value of λ when AC = 17.b. Find the value of λ when is a straight line.c.
Relative to an origin O, the position vectors of points A, B and C are -5i – 11j, 23i – 4j and λ(I – 3j) respectively.Given that C les on the line AB, find the value of λ.
Relative to an origin O, the position vector of A isAnd the position vector of B isThe point A, B and C are such that BC(vector) = 2AB(vector). Find the position vector of C. 3
Relative to an origin O, the position vector of A is 3i – 2j and the position vector of B is 15i + 7j.a. Find AB(vector).The point C lies on AB such that AC(vector) = 1/3 AB(vector).b. Find the
Relative to an origin O, the position vector of A is 6i + 6j and the position vector of B is 12i – 2j.a. Find AB(vector).The point C lies on AB such that AC(vector) = ¾ AB(vector).b. Find the
At time t = 0, boat P leaves the origin and travels with velocity (3i + 4j) km h-1. Also at time t = 0, boat Q leaves the point with position vector (-10i + 17j) km and travels with velocity (5i +
At 12:00 hours two boats, A and B, have position vectors (-10i + 40j) km and (70i + 10j) km and are moving with velocities (20i + 10j) km h-1 and (-10i + 30j) km h-1 respectively.a. Find the position
Find λ and µ such that λa + µb = c.a = 5i – 6j, b = - I + 2j and c = - 13i + 18j.
a. The vectors p and q are such that p = 11i – 24j and q = 2i + αj.i. Find the value of each of the constants α and β such that p + 2q = (α + β)I – 20j.ii. Using the values of α and β

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