Chapter Study

BCA Semester 2 – Mathematics II – Unit 2: Differentiation (6Hrs)

Comprehensive questions and detailed answers for Unit 2: Differentiation (6Hrs). Perfect for exam preparation and concept clarity.

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Find dydx\dfrac{dy}{dx} when x=a(t+sin⁡t),y=a(1−cos⁡t)x = a(t+\sin t), \quad y = a(1-\cos t)

MediumNumerical5 marks2022(TU FOHSS Final)

State L'Hospital's Rule. Use it to evaluate:

lim⁡x→0xex−ln⁡(1+x)x2\lim_{x \to 0} \frac{x e^x - \ln(1+x)}{x^2}
MediumNumerical5 marks2022(TU FOHSS Final)

Find the derivative of y=e3x−1y = e^{3x-1} by the definition method.

MediumNumerical5 marks2023(TU FOHSS Final)

Find dydx\dfrac{dy}{dx} if
a) x=t2−1,y=t4−1x = t^2 - 1,\quad y = t^4 - 1

b) x2+y2=sin⁡xyx^2 + y^2 = \sin xy

MediumNumerical5 marks2024(TU FOHSS Final)

Find the derivative of e−2xe^{-2x} using the first principle.

−∑e−z22-\sum e^{-\frac{z^2}{2}}
MediumTHEORY5 marks2024(TU FOHSS Final)
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Sample Questions

Find \( \dfrac{dy}{dx} \) when \(x = a(t+\sin t), \quad y = a(1-\cos t) \)

Marks: 5Chapter: Unit 2: Differentiation (6Hrs)

State L'Hospital's Rule. Use it to evaluate: \[ \lim{x \to 0} \frac{x e^x - \ln(1+x)}{x^2} \]

Marks: 5Chapter: Unit 2: Differentiation (6Hrs)

Find the derivative of \( y = e^{3x-1} \) by the definition method.

Marks: 5Chapter: Unit 2: Differentiation (6Hrs)

Find \( \dfrac{dy}{dx} \) if a) \( x = t^2 - 1,\quad y = t^4 - 1 \] b) \( x^2 + y^2 = \sin xy \]

Marks: 5Chapter: Unit 2: Differentiation (6Hrs)

Find the derivative of $e^{-2x}$ using the first principle. $$ -\sum e^{-\frac{z^2}{2}} $$

Marks: 5Chapter: Unit 2: Differentiation (6Hrs)

Unit 2: Differentiation (6Hrs) chapter questions with answers for Mathematics II (BCA Semester 2). Prepare for TU exams with our comprehensive question bank and model answers.