Class 12

Math

Calculus

Continuity and Differentiability

Is the function defined by $f(x)={x+5x−5 ifx≤1ifx>1 $ a continuous function?

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The general solution of the D.E. $(x−y)dy+(x+y)dx$ is

The general solution of the D.E. $dxdy +xy =x_{2}$ is

If x and y are connected parametrically by the equations given, without eliminating the parameter, Find $dxdy $.$x=cosθ−cos2θ,y=sinθ−sin2θ$

Differentiate the following w.r.t x.(i) $3x+2 +(2x_{2}+4 1 )$ (ii) $e_{sec_{2}(x)}+3cos_{−1}(x)$ (iii) $g_{7}(gx)$

Differentiate the functions with respect to x , $cos(sinx)$

Find the general solution of each of the following differential equations:$x1+y_{2} dx+y1+x_{2} dy=0$.

Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.

Find the particular solution of the differential equation $x(1+y_{2})dx−y(1+x_{2})dy=0$, given that $y=1$ when $x=0$.