On their son Geoffrey's 11th birthday,Mr and Mrs Shum deposited $600 into an account earning 5%p.a interest compounded annually.They will continue to deposit $600 on each of his successive birthdays, upto and including his 21st birthday, giving him the accumlated funds as a present on his 21stbirthday. i)Show that the amount of Geoffrey's 21st birthday present was $8524.(to the nearest dollar)? ii)What single deposit on Geoffrey's 11thbirthday would have, under the same conditions provided the same 21st birthday present?
The diagram shows the derivative ofy=f(x) i)Write down the x co-ordinate of the turning point on y=f(x) and state wheather its maximum or minimum turning point. ii)At what x value on y=f(x) is there a horizontal point of inflexion? iii)Where is the function y=f(x) increasing? iv)Sketch a Possible graph of y=f(x).
Find the shaded area shown for the curve y = 2sin 2x :
In the diagram above AD ⊥BC and BE ⊥AC . if BE =11 , AD =9 and CD =8 find the length of CE , ensuring you give all necessary eason
Find the area of bounded by the curve y=sec2x,y=x and the lines x=0 and x=π4. leave your anwer in exact form
Which decreasing function shows positive second derivative for all x values?
(A)
(B)
(C)
(D)
Select two statements that are true for the point A shown on the function below?
1.f'(x)<0 2.f'(x)>0 3.f'(x)=0 4.f''(x)<0 5.f''(x)>0 6.f''(x)=0
Find the exact shaded area below:
,
(i) State the equation of the semicircle shown above.
(ii) State the domain of this function.
(iii) State the function of this range.
Calculate in terms of π the length of the arc BC of the sector with centre A.
Calculate the area of the segment between the straight line BC and the arc of the sector, correct to the nearest 0.1cm².
Find the area of the rectangle OQRM in terms of e, if the coordinates of M are (3,0). Find the shaded area POR in terms of e. The section of the curve y=ex from P to R is rotated 360° about the x-axis to form a'solid. Calculate the exact volume of the solid generated.
For the curve
y=13x3-9x+2 Find the stationary points and determine their nature. By solving y"=0 we can see that there may be an inflexion point atx= 0 . What else must be done to show that (0,2) is an inflexion point? Sketch the curve in the domain -4≤x≤4, showing all essential features (there is no need to find the x-intercept).
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