Mathematics Functions and Notations Quiz

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What is the solution of $1 \rac{1}{1+x^2} dx$?

$0$

$1$

$x = 1$

$ ext{sin } x$ (correct)

What does $rac{d}{dx} \rac{x^2}{2}$ equal to?

$x^2 dx$

$3x^2 dx$ (correct)

$x^2 - 1$

$3x + 1$

What is the integral of $tan(3x) \rac{ln 3}{4} dx$?

$x + c$

$rac{1}{4}$

$ ext{ln(sin } x) + c$

$rac{ ext{ln } 3}{4} sec^2 4$ (correct)

What is the slope of a line parallel to the x-axis?

$0$ Signup and view all the answers

Under what condition will the lines represented by $ax^2 + 2hxy + by^2 = 0$ be perpendicular (orthogonal)?

$h^2 - ab = 0$ Signup and view all the answers

What is the range of the function 𝑓(𝑥) = √𝑥^2 − 9?

-1 Signup and view all the answers

What is the derivative of 𝑐𝑜𝑠(𝑥) with respect to 𝑐𝑜𝑠(𝑥)?

0 Signup and view all the answers

If 𝐟(𝐱) = 𝑐𝑜𝑠(𝐱), then what is the derivative 𝐟 ′ ( )?

sec 2 x + c Signup and view all the answers

If the function 𝑓(𝑥) has a maximum value at 𝑥 = 𝑐, then what is the value of 𝐟 ′ (𝑐)?

1 Signup and view all the answers

What is the integral of 𝑡𝑎𝑛(𝑥) with respect to 𝑡𝑎𝑛(𝑥)?

-1 Signup and view all the answers

What is the domain of the function f: X→Y defined by f(x) = C, ∀ x ∈X, y∈Y?

X Signup and view all the answers

If f: X→Y is a function, then what is X called?

Domain Signup and view all the answers

What is the range of the function f(x) = √𝒙 + 𝟐 for x ≥ 1?

[1, +∞) Signup and view all the answers

Which one represents Leibniz notation for the derivative of f(x)?

$𝒅𝒇 𝒅𝒙$ Signup and view all the answers

What is the derivative of tan(x) with respect to tan(x)?

1 Signup and view all the answers

What is the solution of the differential equation 𝑦dx+xdy=0?

xy=c Signup and view all the answers

If the function 𝑓(𝑥) has a maximum value at 𝑥 = 𝑐, then what is the value of 𝐟 ′ (𝐱)?

Zero Signup and view all the answers

What is the equation of a horizontal line through the point (𝟑, 𝟏)?

y = 1 Signup and view all the answers

What is the range of the function 𝑓(𝑥) = √𝑥^2 − 9?

[0,+∞) Signup and view all the answers

What is the derivative of 𝑐𝑜𝑠(𝑥) with respect to 𝑐𝑜𝑠(𝑥)?

0 Signup and view all the answers

Mathematics Functions and Notations Quiz

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Questions and Answers

What is the solution of $1 \rac{1}{1+x^2} dx$?

What does $rac{d}{dx} \rac{x^2}{2}$ equal to?

What is the integral of $tan(3x) \rac{ln 3}{4} dx$?

What is the slope of a line parallel to the x-axis?

Under what condition will the lines represented by $ax^2 + 2hxy + by^2 = 0$ be perpendicular (orthogonal)?

What is the range of the function 𝑓(𝑥) = √𝑥^2 − 9?

What is the derivative of 𝑐𝑜𝑠(𝑥) with respect to 𝑐𝑜𝑠(𝑥)?

If 𝐟(𝐱) = 𝑐𝑜𝑠(𝐱), then what is the derivative 𝐟 ′ ( )?

If the function 𝑓(𝑥) has a maximum value at 𝑥 = 𝑐, then what is the value of 𝐟 ′ (𝑐)?

What is the integral of 𝑡𝑎𝑛(𝑥) with respect to 𝑡𝑎𝑛(𝑥)?

What is the domain of the function f: X→Y defined by f(x) = C, ∀ x ∈X, y∈Y?

If f: X→Y is a function, then what is X called?

What is the range of the function f(x) = √𝒙 + 𝟐 for x ≥ 1?

Which one represents Leibniz notation for the derivative of f(x)?

What is the derivative of tan(x) with respect to tan(x)?

What is the solution of the differential equation 𝑦dx+xdy=0?

If the function 𝑓(𝑥) has a maximum value at 𝑥 = 𝑐, then what is the value of 𝐟 ′ (𝐱)?

What is the equation of a horizontal line through the point (𝟑, 𝟏)?

What is the range of the function 𝑓(𝑥) = √𝑥^2 − 9?

What is the derivative of 𝑐𝑜𝑠(𝑥) with respect to 𝑐𝑜𝑠(𝑥)?

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