Overview (Leaving Cert Applied Maths): Quizzes

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What is the integral of xnx^n using the power rule?

xn+1n+1+c\frac{x^{n+1}}{n+1} + c

What is the integral of 1x\frac{1}{x}?

ln⁡x+c\ln x + c

What is the integral of 1ax+b\frac{1}{ax + b}?

1aln⁡(ax+b)+c\frac{1}{a}\ln(ax + b) + c

What does the fundamental theorem of calculus state for ∫abf(x)dx\int_a^b f(x)dx?

F(b)−F(a)F(b) - F(a)

In the INLATE rule for integration by parts, what does 'N' stand for?

Natural logarithms

How is velocity vv related to distance s(t)s(t)?

v=dsdtv = \frac{ds}{dt}

How is acceleration aa related to distance ss?

Second derivative of distance

What formula calculates work done by a variable force from position aa to bb?

W=∫abF(x)dxW = \int_a^b F(x)dx

What is the first step in solving first-order differential equations?

Separating variables

What distinguishes a particular solution from a general solution?

Initial conditions determine constant

For second-order DEs, if v=dydxv = \frac{dy}{dx}, what does d2ydx2\frac{d^2y}{dx^2} become?

vdvdyv\frac{dv}{dy}

Which is a common examination pitfall to avoid in calculus problems?

Forgetting constant of integration

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Calculus & Differential Equations

Differential Equations

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Calculus & Differential Equations

Differential Equations

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Calculus & Differential Equations

Differential Equations

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Calculus & Differential Equations

Differential Equations

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