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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