Area Under Curve

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What is the equation of the tangent line at the origin for the curve y = x² - x?

x + y = 1

x - y = 0

x + y = 0 (correct)

y = x

What is the x-intercept of the curve y = x² - x?

(0, 1) and (1, 0)

(0, 0) and (2, 0)

(1, 0) and (2, 0)

(0, 0) and (1, 0) (correct)

What is the y-intercept of the curve y = x² - x?

(0, 0) only (correct)

(0, 0) and (0, 1)

(1, 0) and (0, 0)

(0, 0) and (0, 2)

What is the axis of symmetry for the parabola y = 8x?

x = 0 (A) Signup and view all the answers

What is the point of local minima for the curve y = x² - x?

x = 1 (C) Signup and view all the answers

What is the condition for a curve to pass through the origin?

The equation of the curve contains no constant term (C) Signup and view all the answers

What do the points of intersection of the curve with the axes represent?

The points where the curve cuts the axes (B) Signup and view all the answers

What is the condition for a tangent line to be parallel to the x-axis?

dy/dx = 0 (A) Signup and view all the answers

What is the method to find the region of the curve?

Write the equation in the form y = f(x) and find the minimum and maximum values of x (D) Signup and view all the answers

What is the condition for the curve to not exist in a region?

The value of y is imaginary (B) Signup and view all the answers

What can be said about the curve represented by the equation y^2 = 4ax when x is negative?

It does not exist. (A) Signup and view all the answers

What is the first step in finding the region represented by a linear inequality ax + by ≤ c?

Convert the inequality into equality to obtain a linear equation in x, y. (B) Signup and view all the answers

What is the equation of a circle with centre at the origin and radius r?

x^2 + y^2 = r^2 (D) Signup and view all the answers

What is the method to find the points where a straight line meets with the coordinate axes?

By putting x = 0 and y = 0 respectively in its equation. (B) Signup and view all the answers

What can be said about the curve represented by the equation a^2y^2 = x^2(a - x) when x > a?

It does not exist. (D) Signup and view all the answers

What is the region represented by the inequality 3x + 4y ≤ 12?

The region that contains the origin (B) Signup and view all the answers

What is the equation of the tangent at the origin for the curve y = x² - x?

x + y = 0 (B) Signup and view all the answers

What is the vertex of the parabola y = 8x?

(0, 0) (A) Signup and view all the answers

What is the x-intercept of the curve y = x² - x?

Both (0, 0) and (1, 0) (B) Signup and view all the answers

What is the focus of the parabola y = 8x?

(2, 0) (D) Signup and view all the answers

What is the purpose of finding the points where a straight line meets with the coordinate axes?

To graph a straight line (C) Signup and view all the answers

What is the effect of a negative value of x on the curve represented by the equation y² = 4ax?

The curve does not exist on the left side of the y-axis (B) Signup and view all the answers

What is the next step after converting a linear inequality into equality to obtain a linear equation in x, y?

Draw the straight line represented by it (C) Signup and view all the answers

What is the equation of a circle having centre at (0,0) and radius r, in terms of x and y?

x² + y² = r² (B) Signup and view all the answers

What is the region represented by a linear inequality divided into after drawing the straight line?

Two unequal parts (C) Signup and view all the answers

What is the condition for a curve to pass through the origin?

The equation of the curve does not contain constant terms (B) Signup and view all the answers

How do you find the points of intersection of a curve with the x-axis?

By putting y = 0 in the equation of the curve (C) Signup and view all the answers

What does the point of intersection of a curve with the x-axis represent?

The point where the curve intersects the x-axis (C) Signup and view all the answers

What is the condition for a tangent line to be parallel to the x-axis?

The slope of the tangent line is zero (A) Signup and view all the answers

What do you do to find the region of a curve?

Write the given equation as y = f(x) and find minimum and maximum values of x (D) Signup and view all the answers

Area Under Curve

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Questions and Answers

What is the equation of the tangent line at the origin for the curve y = x² - x?

What is the x-intercept of the curve y = x² - x?

What is the y-intercept of the curve y = x² - x?

What is the axis of symmetry for the parabola y = 8x?

What is the point of local minima for the curve y = x² - x?

What is the condition for a curve to pass through the origin?

What do the points of intersection of the curve with the axes represent?

What is the condition for a tangent line to be parallel to the x-axis?

What is the method to find the region of the curve?

What is the condition for the curve to not exist in a region?

What can be said about the curve represented by the equation y^2 = 4ax when x is negative?

What is the first step in finding the region represented by a linear inequality ax + by ≤ c?

What is the equation of a circle with centre at the origin and radius r?

What is the method to find the points where a straight line meets with the coordinate axes?

What can be said about the curve represented by the equation a^2y^2 = x^2(a - x) when x > a?

What is the region represented by the inequality 3x + 4y ≤ 12?

What is the equation of the tangent at the origin for the curve y = x² - x?

What is the vertex of the parabola y = 8x?

What is the x-intercept of the curve y = x² - x?

What is the focus of the parabola y = 8x?

What is the purpose of finding the points where a straight line meets with the coordinate axes?

What is the effect of a negative value of x on the curve represented by the equation y² = 4ax?

What is the next step after converting a linear inequality into equality to obtain a linear equation in x, y?

What is the equation of a circle having centre at (0,0) and radius r, in terms of x and y?

What is the region represented by a linear inequality divided into after drawing the straight line?

What is the condition for a curve to pass through the origin?

How do you find the points of intersection of a curve with the x-axis?

What does the point of intersection of a curve with the x-axis represent?

What is the condition for a tangent line to be parallel to the x-axis?

What do you do to find the region of a curve?

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