if equation of tangent drawn to the curve `y=f(x)` at its point `P(3,5)` is `5x-4y+5=0` and `lim_(x-> 3) {3^(4f(x))-2(1+3+3^2+3^3+..........+3^19)-1}^2 /(1-cos(ln(4-x))) = 2(a*3^b*lnc)^2` where `a,&c ` are prime numbers and `bepsilonN,`then find the value `a+b+c`

if equation of tangent drawn to the curve y=f(x) at its point P(3,5) is 5x-4y+5=0 and lim_(x rarr3)({3^(4f(x))-2(1+3+3^(2)+3^(3)+.........+3^(19))-1}^(2))/(1-cos(ln(4-x)))=2(a*3^(b)*ln c)^(2) where a,&c are prime numbers and b varepsilon N, then find the value a+b+c

If the equation of the tangent to the curve y^(2)=ax^(3)+b at point (2,3) is y=4x-5 then find the values of a and b

Find the length of the tangent for the curve y=x^(3)+3x^(2)+4x-1 at point x=0.

Find the equation of the tangent line to the curve y=sqrt(5x-3)-2 which is parallel to the line 4x-2y+3=0

Find the equation of the tangent line to the curve y=sqrt(5x-3)-2 which is parallel to the line 4x-2y+3=0 .

Equation of the tangent at (1,-1) to the curve x^(3)-xy^(2)-4x^(2)-xy+5x+3y+1=0 is

Equation of the tangent at (1,-1) to the curve x^(3)-xy^(2)-4x^(2)-xy+5x+3y+1=0 is

The equation of the tangent at (2,3) on the curve y^(2)=ax^(3)+b is y=4x-5. Find the values of a and b

The equation of the tangent at (2,\ 3) on the curve y^2=a x^3+b is y=4x-5 . Find the values of a and b .

If the equation of the normal to the curve y=f(x) at x =0 is 3x-y+3=0 then the value of lim_(x rarr0)(x^(2))/({f(x^2)-5f(4x^(2))+4f(7x^(2))}) is