1. f(x)=1sinx,g(x)=1tanx,h(x)=x f(x)=\frac{1}{\sin x}, g(x)=\frac{1}{\tan x}, h(x)=x f(x)=sinx1,g(x)=tanx1,h(x)=x
Find the value of limx→24−x23−x2+5 \lim _{x \rightarrow 2} \frac{4-x^{2}}{3-\sqrt{x^{2}+5}} limx→23−x2+54−x2.
Find the derivative of f(x)g(x) \frac{f(x)}{g(x)} g(x)f(x) with respect to x x x from first principle.
Show that maximum value of h(x)+1h(x) h(x)+\frac{1}{h(x)} h(x)+h(x)1 is smaller than its minimum value.
2. A(2,4),B(3,1),C(4,5);2x−y+2=0 \mathrm{~A}(2,4), \mathrm{B}(3,1), C(4,5) ; 2 x-y+2=0 A(2,4),B(3,1),C(4,5);2x−y+2=0,x−2y+3=0. x-2 y+3=0 \text {. } x−2y+3=0.
If the distances of the point (2,4) (2,4) (2,4) from the y y y-axis and the point (k,4) (k, 4) (k,4) are equal, find k k k.
Find the co-ordinates of the foot of the perpendicular drawn from the point C C C to the straight line AB A B AB.
According to the stem, find the area of the triangle which is formed by the equation of the bisector of the acute angle between the lines and the axis of co-ordinates.
3. x2+y2+6x+8y+21=0,x2+y2=9;x+y=6 \\ x^{2}+y^{2}+6 x+8 y+21=0, x^{2}+y^{2}=9 ; x+y=6 x2+y2+6x+8y+21=0,x2+y2=9;x+y=6
According to the stem, how many numbers can be formed using the co-efficients of x2,y2,x x^{2}, y^{2}, x x2,y2,x and y y y of the first circle together.
Show that, the circles of the stem touch externally at the point (−95,−125) \left(-\frac{9}{5},-\frac{12}{5}\right) (−59,−512).
Find the length of the chord intercepted on the x x x-axis by the circle which passes through the centre of the second circle of the stem and the point of intersection of Ist circle and the straight line of the stem.
4.
Find derivative of x3sin(lnx) x^{3} \sin (\ln x) x3sin(lnx) with respect to x x x.
Using the stem find the value: cos2α+cos2β+cos2γ−2cosαcosβcosγ \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma-2 \cos \alpha \cos \beta \cos \gamma cos2α+cos2β+cos2γ−2cosαcosβcosγ.
Find the area bounded by the region of the stem marked with line segments.
5. P⃗=3i^−3j^+4k^,Q⃗=3i^−2j^+4k^ \vec{P}=3 \hat{i}-3 \hat{j}+4 \hat{k}, \vec{Q}=3 \hat{i}-2 \hat{j}+4 \hat{k} P=3i^−3j^+4k^,Q=3i^−2j^+4k^ and R⃗=i^−j^+ \vec{R}=\hat{i}-\hat{j}+ R=i^−j^+2k^ 2 \hat{\mathrm{k}} 2k^.
Find the vector equation of a straight line passing through the point P→ \overrightarrow{\mathrm{P}} P and parallel to the vector Q→ \overrightarrow{\mathrm{Q}} Q.
Show that, the vector P→−Q→ \overrightarrow{\mathrm{P}}-\overrightarrow{\mathrm{Q}} P−Q is perpendicular to the vector which is perpendicular to the plane formed with P⃗ \vec{P} P and Q⃗. \vec{Q} . Q.
According to the stem if A A A is a matrix formed with the coefficients of i^,j^,k^ \hat{i}, \hat{j}, \hat{k} i^,j^,k^ then find A−1 A^{-1} A−1.
