This is the last question on my calculus 2 final exam! I asked my calculus students to find the slope of the tangent line, the area under the curve, and the arc length of the hyperbolic cosine function cosh(x). Notice the graph of y=cosh(x) is very similar to the parabola y=x^2+1 because the power series expansion for cosh(x) is 1+x^2/2+x^4/4+... The graph of a hyperbolic cosine function is called a catenary (the shape of a hanging chain). I hope my calculus 2 students enjoy this equation and appreciate the cool properties that cosh(x) has! Dear calculus teachers, feel free to put this question on your calculus tests and let me know your students' reactions! : )
#calculus #catenary

the last lecture in my calc 1 class 👉    • finding the volume of a Krispy Kreme ...  
why arc length = area for cosh(x) 👉    • Area under the curve equals to the ar...  

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0:00 the story behind this question
0:33 find the slope of the tangent line to y=cosh(x) at x=4
2:17 find the area under y=cosh(x) from x=0 to x=4
3:31 find the arc length of y=cosh(x) from x=0 to x=4
5:31 why cosh(x) is super cool

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