In this section, we are going to see some questions on binomial expansion including exponential functions and logarithmic functions.
(1) Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid.
(i) 1/(5 + x) Solution
(ii) 2/(3 + 4x)2 Solution
(iii) (5 + x2)2/3 Solution
(iv) (x + 2)-2/3 Solution
(2) Find 3√1001 approximately (two decimal places).
(3) Prove that 3√(x3 + 6) − 3√(x3 + 3) is approximately equal to 1/x2 when x is sufficiently large. Solution
(4) Prove that √(1−x)/(1+x) is approximately equal to 1 − x + x2 when x is very small. Solution
(5) Write the first 6 terms of the exponential series
(i) e5x Solution
(ii) e−2x Solution
(iii) e(1/2)x Solution
(6) Write the first 4 terms of the logarithmic series
(i) log (1 + 4x) Solution
(ii) log(1 − 2x) Solution
(iii) log [(1+3x)/(1−3x)] Solution
(iv) log [(1-2x)/(1+2x)] Solution
(7) If y = x + x2/2 + x3/3 + x4/4 + · · · , then show that x = y − y2/2! + y3/3! − y4/4! + · · · . Solution
(8) If p − q is small compared to either p or q, then show that
(9) Find the coefficient of x4 in the expansion of (3−4x+x2)/e2x . Solution
(10) Find the value of
Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.
You can also visit the following web pages on different stuff in math.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
Analytical geometry calculators
MATH FOR KIDS
Word problems on linear equations
Trigonometry word problems
Word problems on mixed fractrions
Ratio and proportion shortcuts
Converting repeating decimals in to fractions