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As you know Computer Science is a very interesting subject, so in this article we have shared Bsc 1 Year Important Questions of Differential Calculus 2024

Which will help you in studying, if you memorize these Important Questions mentioned in this article, then you can understand upto 60% syllabus, so friends, Read complete list of Bsc 1 Year Important Questions of Differential Calculus 2024, till the end.

## Bsc 1 Year Important Questions of Differential Calculus 2024

**Limits and Continuity:**

Define the concept of a limit. Evaluate limx→2×2−4x−2\lim_{x \to 2} \frac{x^2 – 4}{x – 2}limx→2x−2×2−4.

Explain the epsilon-delta definition of a limit.

Discuss the concept of continuity and determine if the function f(x)=1xf(x) = \frac{1}{x}f(x)=x1 is continuous at x=0x = 0x=0.

**Derivatives:**

Define the derivative of a function. Find the derivative of f(x)=x3−5x+4f(x) = x^3 – 5x + 4f(x)=x3−5x+4.

Explain the geometric interpretation of a derivative.

Differentiate the following functions:

f(x)=sin(x)+cos(x)f(x) = \sin(x) + \cos(x)f(x)=sin(x)+cos(x)

f(x)=e2xf(x) = e^{2x}f(x)=e2x

f(x)=ln(x2+1)f(x) = \ln(x^2 + 1)f(x)=ln(x2+1)

**Rules of Differentiation:**

State and prove the product rule. Use it to differentiate f(x)=x2⋅exf(x) = x^2 \cdot e^xf(x)=x2⋅ex.

State and prove the quotient rule. Use it to differentiate f(x)=sin(x)x2f(x) = \frac{\sin(x)}{x^2}f(x)=x2sin(x).

Differentiate the composite function f(x)=tan(x2+1)f(x) = \sqrt{\tan(x^2 + 1)}f(x)=tan(x2+1) using the chain rule.

**Higher-Order Derivatives:**

Define higher-order derivatives. Find the second derivative of f(x)=x4−3×2+2f(x) = x^4 – 3x^2 + 2f(x)=x4−3×2+2.

Find the third derivative of f(x)=sin(x)f(x) = \sin(x)f(x)=sin(x).

**Rolle’s Theorem and Mean Value Theorem:**

State and prove Rolle’s Theorem. Verify it for f(x)=x3−3xf(x) = x^3 – 3xf(x)=x3−3x on the interval [−1,1][-1, 1][−1,1].

State and prove the Mean Value Theorem (MVT). Apply MVT to the function f(x)=x2+xf(x) = x^2 + xf(x)=x2+x on the interval [1,3][1, 3][1,3].

**Maxima and Minima:**

Explain the concepts of local maxima and minima. Find the local maxima and minima of f(x)=x3−3×2+4f(x) = x^3 – 3x^2 + 4f(x)=x3−3×2+4.

Use the second derivative test to determine the concavity of the function f(x)=x4−4×3+6×2−24x+5f(x) = x^4 – 4x^3 + 6x^2 – 24x + 5f(x)=x4−4×3+6×2−24x+5.

**Curve Sketching:**

Sketch the curve for f(x)=1xf(x) = \frac{1}{x}f(x)=x1. Discuss its asymptotes.

Sketch the curve for f(x)=x3−3xf(x) = x^3 – 3xf(x)=x3−3x. Identify critical points, points of inflection, and intercepts.

**Polar Coordinates:**

Convert the Cartesian coordinates (3, 4) to polar coordinates.

Find the derivative dydx\frac{dy}{dx}dxdy if r=2sin(θ)r = 2\sin(\theta)r=2sin(θ).

**Implicit Differentiation:**

Explain implicit differentiation. Use it to find dydx\frac{dy}{dx}dxdy if x2+y2=25x^2 + y^2 = 25×2+y2=25.

**Related Rates:**

Solve the related rates problem: A ladder 10 feet long is leaning against a wall. If the bottom of the ladder is pulled away from the wall at a rate of 1 ft/sec, how fast is the top of the ladder sliding down the wall when the bottom is 6 feet from the wall?

**L’Hôpital’s Rule:**

State L’Hôpital’s Rule. Use it to evaluate limx→0sin(x)x\lim_{x \to 0} \frac{\sin(x)}{x}limx→0xsin(x).

Use L’Hôpital’s Rule to evaluate limx→∞exx2\lim_{x \to \infty} \frac{e^x}{x^2}limx→∞x2ex.

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The above list covers the important questions that may be important for computer exam. By preparing well for these questions, students can cover a large part of their syllabus and perform better in the exam.

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