Differentiation Class 12 OP Malhotra Exe-8I ISC Maths Solutions Ch-8 Solutions. In this article you would learn about parametric functions . Step by step solutions of latest textbook has been given as latest syllabus. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.
Differentiation Class 12 OP Malhotra Exe-8I ISC Maths Solutions Ch-8
| Board | ISC |
| Publications | S Chand |
| Subject | Maths |
| Class | 12th |
| Chapter-8 | Differentiation |
| Writer | OP Malhotra |
| Exe-8(I) | parametric functions |
Exercise- 8I
Differentiation Class 12 OP Malhotra Exe-8I Solution
Que-1: If x = ct, y =c/t.
Sol: Given x = ct … (1)
and y = c/t … (2)
DifF. eqn. (1) & eqn. (2) w.r.t. t ; we have
dx/dt = c & dy/dt = -c/t²
∴ dy/dx=(dy/dt)/(dx/dt) = – (c/t²)/c = -1/t²
Que-2: x=1/(1-t²) , y=1+t²
Sol:
Que-3: x=a(1+t²/1-t²) , y=b(2t/1-t²)
Sol:
Que-4: If x = a (θ + sin θ), y – a{ 1 – cos θ)
Sol: Given x – a (0 + sin θ) …(1)
& y = a{ 1 – cos θ) …(2)
Diff. eqn. (1) & eqn. (2) w.r.t. θ ; we have
Que-5: If x = b sin² θ and y = a cos²θ.
Sol: Given x = b sin² θ …(1)
& y = a cos²θ …(2)
Diff. eqn. (1) & eqn. (2) w.r.t. t ; we have
Que-6: If x = a cos³ t, y = a sin³ t.
Sol: Given x = a cos³ t …(1)
& y = a sin³t …(2)
Diff. eqn. (1) & eqn. (2) w.r.t. t ; we have
Que-7: x = a(cos t + t sin t), y = a(sin t – t cos t).
Sol: Given x = a(cos t + t sin t) …(1)
& y = a(sin t – t cos t) …(2)
Diff. eqn. (1) & eqn. (2) w.r.t. t ; we have
Que-8: x = 3 cos t – 2 cos3 t, y = 3 sin t – 2 sin³t.
Sol: Given x = (3 cos t – 2 cos³ t) …(1)
& y = 3 sin t – 2 sin³t …(2)
Diff. eqn. (1) & eqn. (2) w.r.t. t ; we have
Que-9: Find dy/dx when x = log t, y = sin t.
Sol: Given x = log t …(1)
& y = sin t …(2)
Diff. eqn. (1) & eqn. (2) w.r.t. t ; we
dx/dt = 1/t & dy/dt = cost
∴ dy/dx = (dy/dt)/(dx/dt) = cos t /(1/t) = t cos t
Que-10: If x = a (cos θ + log tan θ/2) and y = a sin θ, find dy/dx at θ = π/3 and θ = π/4.
Sol: Given x = a (cos θ + log tan θ/2 ) … (1)
& y = a sin θ … (2)
Diff. eqn. (1) & eqn. (2) w.r.t. θ ; we have
–: End Differentiation Class 12 OP Malhotra Exe-8I ISC Math Ch-8 Solution :–
Return to :- OP Malhotra ISC Class-12 S Chand Publication Maths Solutions
Thanks
Please share with your friends
