Engineering Mathematics I: Best Books, Practice Problems

On this page, you can find syllabus, best books on Engineering Mathematics I, and practice problems. Study material on Engineering Mathematics 1 is also given here.

• Syllabus
• Best Books

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Study Materials: nth Derivative

Rolle’s Theorem

Indeterminate Forms and L’Hospital Rule

Taylor Series Expansion

Questions and Answers:

Q1: $\lim \limits_{x \to 0} [x] \quad$ [Solution]

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Q2: $\lim \limits_{x \to \frac{3}{2}} [x] \quad$ [Solution]

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Q3: Find $\lim \limits_{x \to 0} \dfrac{|x|}{x}$, if it exists.

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Q4: $\lim \limits_{x \to 0} \dfrac{\sqrt{1+x}-1}{x}\quad$ [Solution]

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Q5: Find the following limit: $\lim \limits_{x \to 0} x \sin \left(\dfrac{1}{x} \right)$ [Solution]

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Q6: Find the value of k for which the function f(x) = $\begin{cases} \dfrac{1-\cos 4x}{8x^2} \,\, \text{ if } x \neq 0 \\ k \quad \quad \quad \quad \text{ if } x=0 \end{cases}$ is continuous at x=0. [Solution]

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Q7: Find the relation between $a$ and $b$ if f(x) = $\begin{cases} \dfrac{\sin((a-1)x)+xe^x}{x} \,\, \text{ if } x \neq 0 \\ b \quad \quad \quad \quad \quad \quad \quad \quad \,\,\, \text{ if } x=0 \end{cases}$ is continuous at x=0.

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Q8: Find the value of k for which the function f(x) = $\begin{cases} \dfrac{\tan 7x}{2x} \,\, \text{ if } x \neq 0 \\ k \quad \quad \quad \text{ if } x=0 \end{cases}$ is continuous at x=0. [Solution]

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Q9: Define the function f(x) = $\begin{cases} x^2 \cos \left(\dfrac{1}{x} \right) \, \text{ if } x \neq 0 \\ 0 \quad \quad \quad \quad \,\, \text{ if } x=0 \end{cases}$. Find $f'(0)$. [Solution]

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Q10: Find the n^th derivatives for the functions $x^n, \dfrac{1}{x}, \ln x, \sin x$.

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Q11: State Rolle’s theorem. Verify Rolle’s theorem for the functions below:

1. f(x) = x²+2 on [-2, 2]
2. f(x) = sinx on [-π, π]
3. f(x) = tanx on [-π, π]
4. f(x) = |x| on [-1, 1]

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Q12: State Lagrange mean value theorem. Verify it for the function f(x) = x²+2x+3 on [4, 6].

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Recommended Books

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Some Study Material:

1. nth Derivative
2. Rolle’s Theorem
3. Characteristic Equation of a Matrix
4. Cayley-Hamilton Theorem

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