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Should I use a calculator?

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it is quite likely you won't have access to a calculator actually.
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There’s some value in being able to do math mentally in terms of assessing reasonableness of your answer.

Some of my linear algebra exams in uni did not allow the use of calculators, so that’s something too.

Plus, mental math helps you develop a better intuition for how numbers work broadly. Check out #MathStratChat on Twitter; you may be surprised how much doing arithmetic engages your mathematical understanding.
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Nah, whip out the 89, not the 84. Has capabilities that are more useful for some stuff, especially in calc II and beyond like expanding polynomials in partial fraction decomposition, etc. Nothing wrong with using the calc  as long as you understand how the operation is worked out, in what order, and why.

Edit: in seriousness, the 84 is fine for now but in my calc 2 class I’m currently taking the ti84 students have to do much more work on some problems than the ti89 students. The course technically requires the 89 but some students are hard-headed.

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