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Researcher and Student at CHRIST (Deemed to be University), INDIA.
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Questions

Subject:Pre-Calculus

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Question:

Why do we say that a function is increasing if $$\frac{dy}{dx}>0$$?

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We know that $$\frac{dy}{dx}$$ gives the slope of the tangent at any given point on the function. So, if $$\frac{dy}{dx}>0$$, slope of tangent is positive. That means the function is increasing at that point.

Subject:Set Theory

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Question:

If set $$A=\{(x,y)|x^2+y^2=4\}$$ and set $$B=\{(x,y)|x^2+3y^2=2\}$$, then $$|A\cap B|=?$$

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We can see that the curves $$x^2+y^2=4$$ and $$x^2+3y^2=2$$ intersect at the 4 points $$(-0.707,0.707)$$, $$(0.707,0.707)$$, $$(0.707,-0.707)$$, $$(-0.707,-0.707)$$. Hence, $$|A\cup B|=4$$

Subject:LaTeX

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Question:

Is it possible to create the table of contents and the list of figures in a LaTeX document using inbuilt commands? If yes, give the commands to create the same.

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Yes. It is possible. To create the table of contents: \tableofcontents To create the list of figures: \listoffigures

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