`((x)/(3)-(2)/(5))/((3)/(4)-2x)=(16)/(15)`

Evaluate the following integrals : (i) int(2(x+16)^((1)/(2))+(x+16)^((3)/(4)))/(x(x+16)^((5)/(4)))dx (ii) int(1+x^((1)/(2))-x^((2)/(3)))/(1+x^((1)/(3)))dx

Evaluate the following integrals : (i) int(2(x+16)^((1)/(2))+(x+16)^((3)/(4)))/(x(x+16)^((5)/(4)))dx (ii) int(1+x^((1)/(2))-x^((2)/(3)))/(1+x^((1)/(3)))dx

Simplify :((25)^((3)/(2))x(243)^((3)/(5)))/((16)^((5)/(4))x(8)^((4)/(3)))

Observe the following pattern (1x2)+(2x3)=(2x3x4)/(3)(1x2)+(2x3)+(3x4)=(3x4x5)/(3)(1x2)+(2x3)+(3x4)+(4x5)=(4x5x6)/(3) and find the of (1x2)+(2x3)+(3x4)+(4x5)+(5x6)

lim_(x rarr4)((x^(2)-x-12)^(15))/((x^(3)-8x^(2)+16x)^(7))

lim_(x rarr2)(x^(3)-3x^(2)+4)/(x^(4)-8x^(2)+16)

Solve each of the following equations and also check your result in each case: ((45-2x))/(15)-((4x+10))/5=((15-14 x))/9 5((7x+5)/3)-(23)/3=13-(4x-2)/3 (7x-1)/4-1/3\ (2x-(1-x)/2)=(10)/3 (0. 5(x-0. 4))/(0. 42\ )-(0. 6(x-2. 71))/(0. 42)=x+6. 1

5(x-3)=4(3x-16)

(3x+8)/16-((12x-6)/(15x-30))+x/3=(7x)/12-((2x+16)/32)

(5x+2.15)/(3)=4x+60x=?