a beam of length l is supported at one end. If w is the uniform load per unit length, the bending moment M at a distance x from the end is given by M= 1/2lx- 1/2wx2, find the point on the beam at which the bending moment has maximum value.

Q.7. Find whether the function $\mathrm{cos}\left(2x+\frac{\mathrm{\pi}}{4}\right);\frac{3\mathrm{\pi}}{8}x\frac{5\mathrm{\pi}}{8}$ is increasing or decreasing.

a beam of length l is supported at one end. If w is the uniform load per unit length, the bending moment M at a distance x from the end is given by M= 1/2lx- 1/2wx2, find the point on the beam at which the bending moment has maximum value.

Q.37. Find the equations or tangent and normal to curve $x=1-\mathrm{cos}\theta andy=\theta -\mathrm{sin}\theta $ at $\theta =\frac{\mathrm{\pi}}{4}$.

Q.31. $f\left(x\right)=\mathrm{log}\left(1+x\right)-\frac{x}{1+x},x\ne -1$

Q.32. $f\left(x\right)=\left(x+2\right){e}^{-x}$

Q.6 Show that the normal at any pointe to the curve x = a cos $\theta $ + a $\theta $ sin $\theta $, y = a sin $\theta $ - a $\theta $ cos $\theta $ is at a constant distance from the origin.

y^{2}= 8x+ 3 for which they-coordinate changes 4 times more than coordinate ofx.8) Find the equation of tangent to the curve $4{x}^{2}+9{y}^{2}=36atthepoint(3\mathrm{cos}\theta ,2\mathrm{sin}\theta ).$

Q20. A driver stars a car from a point

Pat time t = 0 seconds and stops at pointQ. The distancex( in metres ) covered by it intseconds is given by r =t$\left(2\frac{t}{3}\right)$. Find the time taken by it to reach^{2}Qand also find the distance betweenPandQ. The driver has stopped the car at the pointQon the roadside to take the call on his mobile phone. Has he done right in doing so ?Q. If at each point on the curve y =

x^{1}–ax^{2}+x+1 the tangent is inclined at an acute angle with positive direction of x axis , then(a) a > 0 (b) a $\le \sqrt{3}$ (c) |a| $\le \sqrt{3}$ (d) none of these