Question

Problems 1-4, Find the tangent line approximation of each function at the given value x = a. 1. f(x) = tanx; at a = \frac{\pi}{4} 2. y = e^{\sqrt{x}}; at a = 1 3. g(x) = \frac{1}{\sqrt{x}}; at a = 3 4. y = \frac{\cot x}{\tan x}; a = 1 5. Let f be a differentiable function such that f(-2) = 3 and f'(-2) = 6. The tangent line to the graph of f at x = -2 can be used to find an approximation to a zero of the function, f. Find the approximation for the value of x such that f(x) = 0. 6. Find the linear approximation for f(\theta) = \sin^2 \theta \text{ for } \theta = \frac{\pi}{4}. Use the linear approximation to estimate \theta = 0.8 and calculate the error. Determine whether the approximation overestimates or underestimates the function.

          Problems 1-4, Find the tangent line approximation of each function at the given value x = a.
1. f(x) = tanx; at a = \frac{\pi}{4}
2. y = e^{\sqrt{x}}; at a = 1
3. g(x) = \frac{1}{\sqrt{x}}; at a = 3
4. y = \frac{\cot x}{\tan x}; a = 1
5. Let f be a differentiable function such that f(-2) = 3 and f'(-2) = 6. The tangent line to the
graph of f at x = -2 can be used to find an approximation to a zero of the function, f. Find the
approximation for the value of x such that f(x) = 0.
6. Find the linear approximation for f(\theta) = \sin^2 \theta \text{ for } \theta = \frac{\pi}{4}. Use the linear approximation to
estimate \theta = 0.8 and calculate the error. Determine whether the approximation overestimates or
underestimates the function.

Problems 1-4, Find the tangent line approximation of each function at the given value x = a.
1. f(x) = tanx; at a = (π)/(4)
2. y = e^√(x); at a = 1
3. g(x) = (1)/(√(x)); at a = 3
4. y = (cotx)/(tanx); a = 1
5. Let f be a differentiable function such that f(-2) = 3 and f'(-2) = 6. The tangent line to the
graph of f at x = -2 can be used to find an approximation to a zero of the function, f. Find the
approximation for the value of x such that f(x) = 0.
6. Find the linear approximation for f(θ) = sin^2 θ for θ= (π)/(4). Use the linear approximation to
estimate θ= 0.8 and calculate the error. Determine whether the approximation overestimates or
underestimates the function.

Added by Belen A.

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