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The derivative of the function f(x) = 3x^2 - 4x + 7 is f'(x) = 6x - 4.

The problem involves finding the value of x in an expression where the greatest common factor (GCF) of two terms is given. The GCF is used to determine the value of x, but the problem cannot be solved without additional information about the variable y.

To find the area of the shaded region, subtract the area of a circle (formed by two semicircles) from the area of the enclosing rectangle.

The equation "\[\sqrt{(M-4)(M+4)} = 3\]" was solved by squaring both sides, expanding, simplifying, and taking the square root to find the solutions M = 5 and M = -5.

To find y when x = 4, substitute x = 4 into the equation y = 2x² - 3x + 1. Solving gives y = 21.

The limit of (1 + 1/x)^x as x approaches infinity is e.

The limit of sin(x)/x as x approaches 0 is 1, determined using L'Hôpital's rule.

The limit of (x² - 1) / (x - 1) as x approaches 1 is 2. This is found by factoring the numerator (difference of squares) and canceling the common factor of (x - 1).

The solution to the equation 25^x = 125 is x = 3/2. Squaring this value gives x^2 = 9/4.

The quadratic equation x^2 - x - 6 = 0 was solved by factoring. The solutions are x = 3 and x = -2.

The solution to 4 + 3 - 6 * (6 - 9) is 25.

The limit of (2x)/(x-7) as x approaches 7 from the right is positive infinity.

Solve the inequality 2x - 7 > 5. Find the solution to the inequality and learn how to isolate the variable. Answer: x > 6

Find the integral of x² + 3x - 2. Solution: (x³)/3 + (3x²)/2 - 2x + C

Calculate the definite integral of sin²(x) from 0 to π. Find the solution to this trigonometric integral problem, demonstrating the use of the identity sin²(x) = (1-cos(2x))/2. The answer is π/2.

Calculate the double integral ∫₀²∫₀¹ x²y dx dy. Step-by-step solution reveals the answer is 2/3.

Find the derivative of the function h(x) = ln(x² + 1) using the chain rule. The derivative is h'(x) = 2x / (x² + 1).

Learn how to find the derivative of the function g(x) = sin(x) * e^x using the product rule of differentiation. The solution reveals that the derivative is g'(x) = e^x (sin(x) + cos(x)).

Learn how to find the derivative of the function f(x) = x² + 3x - 2 using the power rule, constant multiple rule, and sum/difference rule. The derivative is f'(x) = 2x + 3.

Simplify the algebraic expression (a + b)² - (a - b)² using the difference of squares pattern. The solution reveals a simplified expression of 4ab.

Find the sum of the first 1000 natural numbers. This math problem can be solved using the formula for arithmetic series, resulting in a sum of 500,500.

This SEO description explains how to find the derivative of the sum of sine and cosine functions. The problem asks for the derivative of sin(x) + cos(x), and the solution demonstrates the application of the sum rule and basic trigonometric derivatives to arrive at the answer: cos(x) - sin(x).

Learn how to find the limit of the rational function (3x² + 2x) / (x² + 1) as x approaches infinity. The solution reveals a simple technique for evaluating limits at infinity and arrives at the answer: 3.

Find the derivative of the polynomial function f(x) = x³ + 2x² - 5x + 3 using the power rule. The derivative is f'(x) = 3x² + 4x - 5.

Learn how to solve the definite integral ∫₀² (x² + 2x) dx, step-by-step, and discover the answer: 20/3.

Find the derivative of the polynomial function f(x) = x³ + 2x² - 5x + 3 using the power rule. The derivative is f'(x) = 3x² + 4x - 5.

Solve the absolute value inequality |x - 3| ≤ 4. The solution is -1 ≤ x ≤ 7.

Solve for x in the inequality 2x - 7 > 5. The solution is x > 6.

Solve the system of equations 2x + y = 8 and x - y = 1. The solution is x = 3 and y = 2.