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Math Assignments Help: Sample Question & Answer

Excel in math with our expert help. Access Math Assignments Help with sample Q&A for effective learning and academic success.

1. Question:

Solve the following system of linear equations:
   \[
   \begin{align*}
   2x + 3y &= 12 \\
   4x - 2y &= 8
   \end{align*}
   \]

Answer:

To solve the system, we can use the substitution or elimination method. In this case, let's use the elimination method. Multiply the first equation by 2 to make the coefficients of \(y\) in both equations cancel each other out: \[ \begin{align*} 4x + 6y &= 24 \\ 4x - 2y &= 8 \end{align*} \] Subtract the second equation from the first: \[ 8y = 16 \implies y = 2 \] Substitute \(y = 2\) back into one of the original equations, let's use the first: \[ 2x + 3(2) = 12 \implies x = 3 \] So, the solution is \(x = 3\) and \(y = 2\).

2. Question:

Evaluate the definite integral: \[ \int_{0}^{\pi} \sin(x) \,dx \]

Answer:

\[ \int_{0}^{\pi} \sin(x) \,dx = \left[-\cos(x)\right]_{0}^{\pi} = -\cos(\pi) - (-\cos(0)) = 2 \]

3. Question:

Calculate the limit:
   \[
   \lim_{{x \to 0}} \frac{\sin(x)}{x}
   \]

Answer:

This is a standard limit. The limit is equal to 1. \[ \lim_{{x \to 0}} \frac{\sin(x)}{x} = 1 \]

4. Question:

Find the derivative of the following function with respect to \(x\):
   \[
   f(x) = 3x^4 - 8x^3 + 2x^2 - 5
   \]

Answer:

\[
   f'(x) = 12x^3 - 24x^2 + 4x
   \]

5. Question:

Solve the quadratic equation for \(x\):
   \[
   2x^2 - 5x + 3 = 0
   \]

Answer:

To solve the quadratic equation, factor it: \[ (2x - 3)(x - 1) = 0 \] This gives two solutions: \(x = \frac{3}{2}\) and \(x = 1\).

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Math Assignment Examples- Question and Solution

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