Class12 ISC Maths Chapter Continuity and Differentiability Exercise5-8

Class XII ISC Chapter Continuity and Differentiability

Explore our extensive collection of Continuity and Differentiability questions, tailored for class 12 students following the ISC curriculum. This topic is vital for understanding how to optimize a particular outcome given certain constraints. Our practice questions cover various aspects of Linear Programming, including formulating linear inequalities, graphical methods, and finding optimal solutions. Whether you're looking to strengthen your problem-solving skills or prepare for your exams, these questions provide the perfect resource to master Continuity and Differentiability concepts with ease.

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Continuity & Differentiability

Find
dy / dx
in the following (1 to 4):

Q7 Use implicit differentiation to verify that
dy / dx
.
dx / dy
= 1, when
(i) y²=4ax
(ii) x³ + y³ = 3axy.

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Q8 Find
dy / dx
when
(i) y + sin y = cos x
(ii) ax + by² = cos y
(iii) y sec x + tan x + x²y = 0
(iv) sin² x + cos² y = 1
(v) xy + y²= tanx +y
(vi) y = tan (x + y)
(vii) sin(xy) +
x / y
= x² - y
(viii) sec (x + y) = xy.

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Q9 If sec (
x + y / x - y
) = a, prove that
dy / dx
=
y / x

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Q10 (i) y = x sin (a + y), prove that
dy / dx
=
sin²(a+y) / sin (a + y) - y cos(a + y)

(ii) If sin x = y sin (x + a), prove that
dy / dx
=
sin a / sin²(x + a)

(iii) If sin y = x sin (a + y), prove that
dy / dx
=
sin²(a + y) / sin a

View Solution

Q11 (i) If y = √x + √ x + √ x +....∞ prove that (2y - 1)
dy / dx
= 1
(ii) If y = √sinx + √ sinx + √ sinx +....∞ prove that (2y - 1)
dy / dx
= cosx
(iii) If y = √tanx + √ tanx + √ tanx +....∞ prove that (2y - 1)
dy / dx
= sec²x

View Solution

Class XII ISC Chapter Continuity and Differentiability

Select Exercise

Find
dy / dx
in the following (1 to 4):

Q1 (i) x - y = π
(ii) x² + y² = 25.

Q2 (i) xy = c²
(ii)
x² / a²
+
y² / b²
= 2016

Q3 (i) √x + √y = √c
(ii) x³ + x²y + xy² + y³ = 81.

Q4 (i) 2x + 3y=sinx
(ii) 2x + 3y = sin y.

Q5 Find
dy / dx
when
(i) (x² + y²)² = xy
(ii) sin (x + y) = 2/3

Q6 If x^2/3 + y^2/3 = 2, find dy/dx at (1, 1).

Q7 Use implicit differentiation to verify that
dy / dx
.
dx / dy
= 1, when
(i) y²=4ax
(ii) x³ + y³ = 3axy.

Q8 Find
dy / dx
when
(i) y + sin y = cos x
(ii) ax + by² = cos y
(iii) y sec x + tan x + x²y = 0
(iv) sin² x + cos² y = 1
(v) xy + y²= tanx +y
(vi) y = tan (x + y)
(vii) sin(xy) +
x / y
= x² - y
(viii) sec (x + y) = xy.

Q9 If sec (
x + y / x - y
) = a, prove that
dy / dx
=
y / x

Q10 (i) y = x sin (a + y), prove that
dy / dx
=
sin²(a+y) / sin (a + y) - y cos(a + y)

(ii) If sin x = y sin (x + a), prove that
dy / dx
=
sin a / sin²(x + a)

(iii) If sin y = x sin (a + y), prove that
dy / dx
=
sin²(a + y) / sin a

Q11 (i) If y = √x + √ x + √ x +....∞ prove that (2y - 1)
dy / dx
= 1
(ii) If y = √sinx + √ sinx + √ sinx +....∞ prove that (2y - 1)
dy / dx
= cosx
(iii) If y = √tanx + √ tanx + √ tanx +....∞ prove that (2y - 1)
dy / dx
= sec²x

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SERVICES

CONTACT

Class XII ISC Chapter Continuity and Differentiability

Select Exercise

Find dy / dx in the following (1 to 4):

Q1 (i) x - y = π (ii) x2 + y2 = 25.

Q2 (i) xy = c2 (ii) x2 / a2 + y2 / b2 = 2016

Q3 (i) √x + √y = √c (ii) x3 + x2y + xy2 + y3 = 81.

Q4 (i) 2x + 3y=sinx (ii) 2x + 3y = sin y.

Q5 Find dy / dx when (i) (x2 + y2)2 = xy (ii) sin (x + y) = 2/3

Q6 If x2/3 + y2/3 = 2, find dy/dx at (1, 1).

Q7 Use implicit differentiation to verify that dy / dx . dx / dy = 1, when (i) y2=4ax (ii) x3 + y3 = 3axy.

Q8 Find dy / dx when (i) y + sin y = cos x (ii) ax + by2 = cos y (iii) y sec x + tan x + x2y = 0 (iv) sin2 x + cos2 y = 1 (v) xy + y2= tanx +y (vi) y = tan (x + y) (vii) sin(xy) + x / y = x2 - y (viii) sec (x + y) = xy.

Q9 If sec ( x + y / x - y ) = a, prove that dy / dx = y / x

Q10 (i) y = x sin (a + y), prove that dy / dx = sin2(a+y) / sin (a + y) - y cos(a + y) (ii) If sin x = y sin (x + a), prove that dy / dx = sin a / sin2(x + a) (iii) If sin y = x sin (a + y), prove that dy / dx = sin2(a + y) / sin a

Q11 (i) If y = √x + √ x + √ x +....∞ prove that (2y - 1) dy / dx = 1 (ii) If y = √sinx + √ sinx + √ sinx +....∞ prove that (2y - 1) dy / dx = cosx (iii) If y = √tanx + √ tanx + √ tanx +....∞ prove that (2y - 1) dy / dx = sec2x

Reach Us

SERVICES

CONTACT

Find
dy / dx
in the following (1 to 4):

Q1 (i) x - y = π
(ii) x² + y² = 25.

Q2 (i) xy = c²
(ii)
x² / a²
+
y² / b²
= 2016

Q3 (i) √x + √y = √c
(ii) x³ + x²y + xy² + y³ = 81.

Q4 (i) 2x + 3y=sinx
(ii) 2x + 3y = sin y.

Q5 Find
dy / dx
when
(i) (x² + y²)² = xy
(ii) sin (x + y) = 2/3

Q6 If x^2/3 + y^2/3 = 2, find dy/dx at (1, 1).

Q7 Use implicit differentiation to verify that
dy / dx
.
dx / dy
= 1, when
(i) y²=4ax
(ii) x³ + y³ = 3axy.

Q8 Find
dy / dx
when
(i) y + sin y = cos x
(ii) ax + by² = cos y
(iii) y sec x + tan x + x²y = 0
(iv) sin² x + cos² y = 1
(v) xy + y²= tanx +y
(vi) y = tan (x + y)
(vii) sin(xy) +
x / y
= x² - y
(viii) sec (x + y) = xy.

Q9 If sec (
x + y / x - y
) = a, prove that
dy / dx
=
y / x

Q10 (i) y = x sin (a + y), prove that
dy / dx
=
sin²(a+y) / sin (a + y) - y cos(a + y)

(ii) If sin x = y sin (x + a), prove that
dy / dx
=
sin a / sin²(x + a)

(iii) If sin y = x sin (a + y), prove that
dy / dx
=
sin²(a + y) / sin a

Q11 (i) If y = √x + √ x + √ x +....∞ prove that (2y - 1)
dy / dx
= 1
(ii) If y = √sinx + √ sinx + √ sinx +....∞ prove that (2y - 1)
dy / dx
= cosx
(iii) If y = √tanx + √ tanx + √ tanx +....∞ prove that (2y - 1)
dy / dx
= sec²x