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4th/4parts: Maclaurin Series [ahp kia]
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lim x/e^x? as x→∞
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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...
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trig Write each expression as an equivalent algebraic expression involving only x.
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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx
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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(x)) dx
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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx
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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)
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exp Differentiate (i) b^e^x (ii) b^x&e (iii) (b^e)^x (iv) (b^x)^e
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2 ways: sq root derivative 1/(√√(1/√x))
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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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4 ways: sum Find the sum of the values of 4+3i for i=1,2,...,100
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exp integral ∫a^(√√x^3)/√√x dx
2nd Alt. way: log Taylor series of ln(sec(x)) withOUT Taylor series explicitly
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trig integral cos^2(x) sin(x) dx
1st/2parts 3 ways: tn-1 + tn = n^2 where tn = nth triangular number
2 ways: integral (3+5x)/(x(x-1)) dx
trig integral a) Show that sin(t) cos(t)=1/2 sin^2(t)+c
Review: trig sin(x+90)= cos(x) & cos(x+90)=-sin(x)
Review: trig sin(x+180)= -sin(x) & cos(x+180)=-cos(x)