`5(4x+5)=5(x+2(1)/(2))-(1)/(2)(7x+12)`

lim_(x rarr2)((x+2)^((1)/(2))-(15x+2)^((1)/(5)))/((7x+2)^((1)/(4))-x)

Find each of the following products: (i) (x + 3) (x - 3) (ii) (2x + 5)(2x - 5) (ii) (8 + x)(8 - x) (iv) (7x + 11y) (7x - 11y) (v) (5x^(2) + (3)/(4) y^(2)) (5x^(2) - (3)/(4) y^(2)) (vi) ((4x)/(5) - (5y)/(3)) ((4x)/(5) + (5y)/(3)) (vii) (x + (1)/(x)) (x - (1)/(x)) (viii) ((1)/(x) + (1)/(y)) ((1)/(x) - (1)/(y)) (ix) (2a + (3)/(b)) (2a - (3)/(b))

Fill in the blanks :-4x(7)/(9)=(7)/(9)x (ii) (5)/(11)x(-3)/(8)=(-3)/(8)x(1)/(2)x((3)/(4)+(-5)/(12))=(1)/(2)x+dot x(-5)/(12)(-4)/(5)x((5)/(7)+(-8)/(9))=((-4)/(5)x)+(-4)/(5)x(-8)/(9)

If f(x)=(x^(2))/(1.2)-(x^(3))/(2.3)+(x^(4))/(3.4)-(x^(5))/(4.5)+..oo then

If f(x)=(x^(2))/(1.2)-(x^(3))/(2.3)+(x^(4))/(3.4)-(x^(5))/(4.5)+..oo then

(17(2-x)-5(x+12))/(1-7x)=8

x/5+12=(2x+1)/5

Assertion (A) : (1)/(5)+(1)/(3.5^(3))+(1)/(5.5^(5))+(1)/(7.5^(7))+…(1)/(2)log((3)/(2)) Reason (R ) : If |x| lt 1 then log_(e )((1+x)/(1-x))=2(x+(x^(3))/(3)+(x^(5))/(5)+…)