MA103 Lab Report 6 - Shapes of CurvesName:Student Number:Fall 20201. [6marks]Recall the class of functions called hyperbolic functions, one of which is tanh(x) =ex-e-xex+e-x.(a) Identify the indeterminate form oflimx→∞tanhx.limx→∞tanh(x) has the indeterminate form of∞∞.(b) Apply L’Hospital’s rule once tolimx→∞tanh(x) but do not evaluate the resulting limit.limx→∞tanhx= limx→∞ex-e-xex+e-xH= limx→∞ex+e-xex-e-x(c) Notice that the result from part (b) has another indeterminate form. Apply L’Hospital’s rule a second time but do notevaluate the resulting limit.limx→∞ex+e-xex-e-xH= limx→∞ex-e-xex+e-x= limx→∞tanhx(d) Looking at the result in (c), why would we not go ahead and apply L’Hospital’s Rule one more time?The result in (c) is the same as the initial function. L’Hospital’s rule will keep us going around in circles.(e) Re-writelimx→∞tanh(x) using the substitutiont=exand then evaluate the limit using L’Hospital’s rule.Note that whenx→ ∞thent=ex→ ∞as well.