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A grandparent gives a grandchild Β£100 at birth, and promises to increase the gift by Β£5 on each subsequent birthday.
a. Show that the grandchild will receive Β£200 on the 20π‘β birthday.
b. If the child has saved all the money, what is the total amount at age 20?
c. By how much would the gift have to increase each year if the total at age 20 is to be Β£4,200?
a. Expand (π+π)5. Hence find the coefficient of π₯ in the expansion of (4π₯+2/9π₯)5
b. The coefficient of π₯2 in the expansion of (1+π₯)n is 45. Given that π is a positive integer, find the value of π.
The curve π¦=βπ₯3+3π₯2+6π₯β8 cuts the π₯-axis at π₯=β2,π₯=1 and π₯=4.
a. Sketch the curve, showing clearly the intersection with the coordinate axes.
b. Differentiate π¦=βπ₯3+3π₯2+6π₯β8
c. Show that the tangents to the curve at π₯=β2 and π₯=4 are parallel.
A curve is described by π¦=ππ₯2+ππ₯, where π and π are constants.
a. Find an expression for the gradient of this curve at any point.
b. Given that at the point (1,β2) the gradient is 6, calculate the values of π and π.
c. Show that the equation of the normal to the curve at the point (1,β2) can be written as π₯+6π¦+11=0.
QUESTION: A study believes that 70% of adults in the Philippines own a cellphone.
A cellphone manufacturer believes that the actual number is much
less than 70%. 100 Filipino adults were surveyed, of which 74 have
cellphones. Using a 5% level of significance, is the cellphone
manufacturerβs claim valid or not?
CLAIM:
EVIDENCE:
REASONING:
Directions: Draw a conclusion for the given situation using the five-step hypothesis testing
procedure for population proportion in both methods (critical value method and
the p-value method)
1. A nationwide poll claims that the countryβs president has a less than 64% approval rating.
In a random sample of 120 people, 69 of them gave the president a positive approval
rating. Test the claim at 0.05 level of significance.
Show that L(P2, f) <=U(P1, f) where f(x)= 3x + 2 is defined over [1,0] andΒ P1 ={0,1/2,3/4,1} and P2={0,1/4,1/2,3/4,1}
Let a function :f R β R be defined by f(x) =2 if x β Q , 4 if x does not belong to Q. Show that f is not continuous at any x β R.
Consider the function, f defined by f(x)=| x β 3| + [x] x β [2,4] where x] denotes the greatest integer function. Is this function differentiable in ?[2,4]Justify your answer
Show that Rn(x) the Lagrangeβs form of remainder in the Maclaurin series expansion of cos 3x tends to zero as n β β.Hence obtain its infinite Maclaurin expansion.Β
#332078 on Oct 2022