# Functions and Continuity

Calculus Level 4

$f(x)= \begin{cases} \dfrac{a(1-x\sin x) + b\cos x + 5}{x^2}&\text {if } x<0\\ 3& \text{if }x=0\\ \left(1+\left(\dfrac{cx + dx^3}{x^2}\right)\right)^{\frac 1 x} & \text{if }x>0 \end{cases}$

A piecewise function $$f(x)$$ is defined as shown above, where $$a,b,c$$ and $$d$$ be constants.

If $$f(x)$$ is continuous at $$x=0$$, find $$2e^d + 7c-3a-5b$$.

Clarification: $$e \approx 2.71828$$ is the Euler's number.

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