Question

f (x) = -ex + Sinx + 3x = 0 function’s [0; 1] Show that it's a root within the closed range. [0; Obtain a root within the 1] interval using the Newton-Rahpson method with 5 decimal precision (5D).

Answer #1

f(x) = ex - 2x - 1 = 0 function's [1; 2] there's a
root within the closed range Show. Graphs f1 (x) = ex
and f2 (x) = 2x + 1 functions on an equivalent axis Indicate the
situation of the basis by drawing. Functional iteration by taking
x0 = 1.5 (sequential approaches) method with 5 decimal precision
(5D).

Suppose f(x)=x6+3x+1f(x)=x6+3x+1. In this problem, we will show
that ff has exactly one root (or zero) in the interval
[−4,−1][−4,−1].
(a) First, we show that f has a root in the interval
(−4,−1)(−4,−1). Since f is a SELECT ONE!!!! (continuous)
(differentiable) (polynomial) function on the
interval [−4,−1] and f(−4)= ____?!!!!!!!
the graph of y=f(x)y must cross the xx-axis at some point in the
interval (−4,−1) by the SELECT ONE!!!!!! (intermediate value
theorem) (mean value theorem) (squeeze theorem) (Rolle's theorem)
.Thus, ff...

13.1.7. Problem. Let f(x) = sinx and g(x) = cosx for 0 ≤ x ≤ π.
Find du(f,g) in the set of functions B([0, π]).
13.1.8. Problem. Let f(x) = 3x−3x3 and g(x) = 3x−3x2 for 0 ≤ x ≤ 2.
Find du(f,g) in the
set of
functions B([0, 2]).

A.) Find the range of f(x) = 2x+1/x-3 show all workings. B.)
Find the range f(x)=3x-2/x-5 show all workings C.) find the range
of f(x)=1+√x+2

(a) Find the maximum and minimum values of f(x) = 3x 3 − x on
the closed interval [0, 1] by the following steps:
i. Observe that f(x) is a polynomial, so it is continuous on the
interval [0, 1].
ii. Compute the derivative f 0 (x), and show that it is equal to
0 at x = 1 3 and x = − 1 3 .
iii. Conclude that x = 1 3 is the only critical number in...

Find f(x).
1. f''(x) = (1/3) x^3 −3x^2 + 6x
2. f''(x) = −1 + 6x−12x^2, f(0) = 4, f'(0) = 12
3. f'''(x) = sinx, f(0) = 1, f'(0) = 2, f''(0) = 3

Find the Taylor series for f(x) and it's radius of
convergence when f(x) = e^3x and is centered at c = 2. Also find the
interval of convergence.

Let f(x) = x^3 + x - 4
a. Show that f(x) has a root on the interval [1,4]
b. Find the first three iterations of the bisection method on f
on this interval
c. Find a bound for the number of iterations needed of bisection
to approximate the root to within 10^-4

1.
What is the derivative of f(x) = cosx/sinx
2. What is the derivative of f(x) = cos^-1 (3x)
3. What is the second derivative of tanx/secx
4. True or False: If f'(x) = 2^x, then a possible equation for
f is f(x) = 2^x +3
5. True or False: The equation x^2 + y^2 = 100 is an implicit
curve

1. Find the point on the curve y = x2 that is closest to (0,
5).
2. Find the function f(x),iff′′(x)=sinx+x and f(0)=f(π)=0.
3. Find derivatives of the following functions. a) arcsin(
square root 3x)

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