Question

Find a value of k, if any, making h(x) continuous on [0, 5]. $\qquad h(x) = \begin{cases} k \cos x & 0 \le x \le \pi \\ 10 - x & \pi < x \end{cases}$ Note: Type pi to input $\pi$. Enter the exact answer or round it to three decimal places. Enter NA if there is no value of k which makes the function continuous.

          Find a value of k, if any, making h(x) continuous on [0, 5].
$\qquad h(x) = \begin{cases} k \cos x & 0 \le x \le \pi \\ 10 - x & \pi < x \end{cases}$
Note: Type pi to input $\pi$. Enter the exact answer or round it to three decimal places. Enter NA if there is no value of k which makes the function continuous.

Find a value of k, if any, making h(x) continuous on [0, 5].
h(x) = k cos x 0 ≤ x ≤π
10 - x π < x
Note: Type pi to input π. Enter the exact answer or round it to three decimal places. Enter NA if there is no value of k which makes the function continuous.

Added by Albert M.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Dwijendra Rao

05/18/2021

Step 1

Since we want to make h(x) continuous on [0, 5], the left and right limits of h(x) at x = 0 and x = 5 must be equal. At x = 0, we have: lim (x->0+) h(x) = lim (x->0+) 10/(kcosx) = 10/k At x = 5, we have: lim (x->5-) h(x) = lim (x->5-) 10/(kcosx) = Show more…

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Find value of k,if any. making h(x) continuous on [0, 5]. kcos x h(x) = 10 0 <x <t I < * Note: Type pi to input I . Enter the exact answer Or round it t0 three decimal places. Enter NA if there is no value of k which makes the function continuous