need help with A, B, C, D, E, and F
-/10 POINTS SCALCET8 5.TF.006. Determine whether the statement is true or false. 18 If f'is continuous on [7,8], then I f'(v) dv = f(8) - f(7). C True C False Need Help? Talk to a Tutor | -110 POINTS SCALCET8 5.TF.008. Determine whether the statement is true or false. If f and g are differentiable and f(x) = g(x) for a < x < b, then f '(x) > g'(x) for a < x <b. True False Need Help? Talk...
(a) (b) Find the least squares approximation of f(x) = x2 + 3 over the interval [0, 1] by a function of the form y = ae? + bx, where a, b E R. You should write the coefficients a, b as decimal approximations, rounded to two decimal places. Let g(x) be the least squares approximation you found in the pre- vious problem. So g(x) = ae” + bx for some scalars a, b. Find the least squares approximation of...
Determine whether the statement is TRUE or FALSE. You are NOT required to justify your answers. (a) Suppose both f and g are continuous on (a, b) with f > 9. If Sf()dx = Sº g(x)dx, then f(x) = g(x) for all 3 € [a, b]. (b) If f is an infinitely differentiable function on R with f(n)(0) = 0 for all n = 0,1,2,..., then f(x) = 0 for all I ER. (c) f is improperly integrable on (a,...
11. Circle true or false. No justification is needed. (14 points) (a) If f(x) - o(g(x), and both functions are continuous and positive, then fix dz converges. TRUE FALSE (b) If f(x)- o(g(x)), then f(x)gx)~g(x). TRUE FALSE (c) If the power series Σ an(x + 2)" converges atェ= 5, then it must km0 converge at =-6. TRUE FALSE (d) There exists a power series Σ akz" which converges to f(z)-I on some interval of positive length around FALSE TRUE (e)...
Find fY(y) from the domain: Consider the domain D={(x,y): 0 < x < 1,-x < y < x} and let fix, y)=cx,where c is a constant. 1.1 (4.6 marks) To start with, we wish you to determine c such that f(x, y) a joint density of random vector (X, Y) that takes values on D. order to do that, you must first calculate fix, y) dA where dA is an area element of D, and then deduce c Hence you...
For parts a, b, c and d, use the following function: f(x) = e-5x a) (3 points) Write the Taylor polynomial of degree four for f(x) centered at 0. b) (2 points) Use the Taylor polynomial from part a to estimate the value of e-0.5. (Hint: let find x). c) (3 points) Write the series generated by f(x) at zero in sigma notation. d) (3 points) Find the radius of convergence and state the interval of convergence. d) (3 points)...
For the piecewise linear function, find (a) f-3), (b) -2), (c) K0), (d) f(2), and (e) f(5) 2x ifxs-2 fix): x-2 ifx-2 (a) -3) (b) f-2)= (c) f(0)= (d) (2)= (e) 5)-
a. Show that all derivatives d"f/dx of f(x)e are equal to each other and use this to b. Evaluate the derivatives d" f/da of f(x)with a a constant and use this to write c. Prove that the Taylor series in part (b) for f(x)-ea converges for all . Explain explicitly d. How many terms in the Taylor series for єェwith Zo = 0 does it take to approximate the write down the Taylor series for e" about an arbitrary point...
line response. lin0g(x).-3. Namethelimitruiesthatareusedto steps (a) (b), and (c) of the following calculation. x-0 (f(x) +15) 1/2 (b) lim -f)- lim 3gt)(1 lim fix) -3 lim g) lim (-1f(x) -3g(x)) lim (f(x) 15) x--0 (c) x-0 x--0 lim fx)+lim 15)1/2 l (y 15)12( ( 15)1/2 A) (a) Difference Rule (b) Power Rule (c) Sum Rule B) (a) Quotient Rule C) (a) Quotient Rule D) (a) Quotient Rule (b) Difference Rule (c) Constant Multiple Rule (b) Difference Rule, Power Rule (c)...
please do a,b,c 1. True/False-if true, provide a brief explanation and if false, provide a counterexample. a. Every real valued function has a power series representation about each point in its domain. b. Given a polynomial function f(x) with Taylor series T(x) centered at x a, T(x) = f(x) for all values of a. For a parametrically defined curve, x f(t),y g(t), the second derivative is a'y ("(0-r"C) dx C. Hint: recall the formula from the textbook