Show that `2sinx+tanxgeq3x ,w h e r e0lt=x

Evaluate the following integral: int_0^9f(x)dx ,\ w h e r e\ f(x){sinx ,\ 0lt=xlt=pi//2 1,pi/2lt=xlt=3e^(x-3),\ 3lt=xlt=9

Find the area of the region bounded by the x-axis and the curves defined by y=tanx(w h e r e-pi/3lt=xlt=pi/3) and y=cotx(w h e r epi/6lt=xlt=(3x)/2) .

Write the range of the function f(x)=sin[x],w h e r e(-pi)/4lt=xlt=pi/4 .

Show that f(x)={(x-|x|)/(2),2 w h e nx!=0i sd i s con t inuou sa tx=0dotw h e nx=0

Evaluate: int_(-1)^1f(x)dx ,w h e r ef(x)={1-2x ,xlt=0 1+2x ,xgeq0 int_(-1)^4f(x)dx ,w h e r ef(x)={2x+8,1lt=xlt=2 6x ,2lt=xlt=4

Evaluate the following integral: int_2^4f(x)dx ,\ w h e r e\ f(x)={7x+3,\ if\ 1lt=xlt=3 8x ,\ if\ 3lt=xlt=4

Show that the solutions of the equation [x y z t]^2=Oa r e[x y z t]=[+-sqrt(alphabeta)-betaalpha+-sqrt(alphabeta)],w h e r ealpha,beta are libitrary.

Evaluate the following integrals: int_-5^0f(x)dx ,w h e r ef(x)=|x|+|x+2|+|x+5|

Let f(x)=int_1^x(3^t)/(1+t^2)dx ,w h e r e x > 0. Then (a)for 0

Find the following function is differentiable at a given point or not? f(x)=[x\ sinpix]a t\ x=0,\ w h e r e\ [x] denotes the greatest integer less than or equal to x .