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Hyperbolic Functions Solved Problems
Subjects
>
Mathematics
> Hyperbolic Functions
Which problem do you want to solve ?
Given that: `p = bcosh x`, `q = bsinh x`. Show that `(p + q)/(p - q) = e^(2x)`
Show that `sinh y + cosh y = cx` can be written as `y = ln (x) + k` where `c` and `k` are constants.
Prove that: `d/(dx) (coth^(-1) e^x) = -1/2 cosech x`
Prove that: `d/(dx) (e^(2tanh^(-1)x)) = 2(1 - x)^(-2)`
Draw a graph of `y = sech x` and find its domain and range.
Sketch the graph of `f(x) = sech^(-1) (x)` and determine its domain and range.
Prove that: `sinh^(-1) x = ln |x pm sqrt(x^2 - 1)|`
Prove that: `cosh x + sinh x = e^x`
Prove that: `cosh x - sinh x = e^(-x)`
Find the minimum value of `y = 5cosh x + 3sinh x`
Prove that: `cosh (ln x) - sinh (ln x) = 1/x`
Solve for `x` if:
`2tanh^(-1) ((x - 2)/(x + 1)) = ln 2`
If `cos x = tanh u` then prove that: `e^u = cot (x/2)`
If `t = tanh (x/2)`, express `sinh x` and `cosh x` in terms of `t`
Express `sinh^(-1) - ln x` in terms of natural logarithms hence find the limit as `x rarr oo`
If `acosh x + bsinh x = c`. Show that the equation has real solution if `b^2 + c^2 >= a^2`
Show that: `1/(e^(-3ln x)) ( sqrt( (cosh (ln x) - sinh (ln x))/ (cosh (ln x) + sinh (ln x))) ) = x^2`
Solve: `2sech x + 4tanh x + 1 = 0`
Show that: `cosh (m + 1)x - cosh (m - 1)x = 2sinh x * sinh mx`
Find the area of the region bounded by the coordinates axes, the line `x = ln 3` and the curve with the equation `y = cosh 2x + sech^2 x`
Recommended Lessons
Which problem do you want to solve ?
Given that: `p = bcosh x`, `q = bsinh x`. Show that `(p + q)/(p - q) = e^(2x)`
Show that `sinh y + cosh y = cx` can be written as `y = ln (x) + k` where `c` and `k` are constants.
Prove that: `d/(dx) (coth^(-1) e^x) = -1/2 cosech x`
Prove that: `d/(dx) (e^(2tanh^(-1)x)) = 2(1 - x)^(-2)`
Draw a graph of `y = sech x` and find its domain and range.
Sketch the graph of `f(x) = sech^(-1) (x)` and determine its domain and range.
Prove that: `sinh^(-1) x = ln |x pm sqrt(x^2 - 1)|`
Prove that: `cosh x + sinh x = e^x`
Prove that: `cosh x - sinh x = e^(-x)`
Find the minimum value of `y = 5cosh x + 3sinh x`
Prove that: `cosh (ln x) - sinh (ln x) = 1/x`
Solve for `x` if:
`2tanh^(-1) ((x - 2)/(x + 1)) = ln 2`
If `cos x = tanh u` then prove that: `e^u = cot (x/2)`
If `t = tanh (x/2)`, express `sinh x` and `cosh x` in terms of `t`
Express `sinh^(-1) - ln x` in terms of natural logarithms hence find the limit as `x rarr oo`
If `acosh x + bsinh x = c`. Show that the equation has real solution if `b^2 + c^2 >= a^2`
Show that: `1/(e^(-3ln x)) ( sqrt( (cosh (ln x) - sinh (ln x))/ (cosh (ln x) + sinh (ln x))) ) = x^2`
Solve: `2sech x + 4tanh x + 1 = 0`
Show that: `cosh (m + 1)x - cosh (m - 1)x = 2sinh x * sinh mx`
Find the area of the region bounded by the coordinates axes, the line `x = ln 3` and the curve with the equation `y = cosh 2x + sech^2 x`
Recommended Lessons