22. What is the function that has ane variabke which is not defined only in terms of another varable? Loganthmic Fun...
1. Let f:R → R be the function defined as: 32 0 if x is rational if x is irrational Prove that lim -70 f(x) = 0. Prove that limc f(x) does not exist for every real number c + 0. 2. Let f:R + R be a continuous function such that f(0) = 0 and f(2) = 0. Prove that there exists a real number c such that f(c+1) = f(c). 3 Let f. (a,b) R be a function...
Let f be the function defined by F(x)=(1/2)(x+2)^2 for [-2,0) and 2-2sin(sqrtx) for [0, (x^3)/4]. the graph of f is shown in the figure above. Let R be the regiok bounded by the graph of f and the x-axis. for -25=co for osca Let I be the function defined by 1 (2) - {}(2+2) (2-2n The graph of fis shown in the figure above. Let R be the region bounded by the graph off and the ads (a) Find the...
Please answer nos. 9, 10, 11, 12, 13, 17, and 18 and show solution if possible Editing Ado Styles Paragraph 1 10 i 11- 1-12-1 tǐ3-1n: 14: 1-15-i 16. itt17. I en 193 Font u19, -11. I .. 12. I '13, 1 . 14. I "15- I :16, 1 .17.. rectangle of perimeter 24 cm about one of its sides What 17. The base of an isosceles triangle is 8 m long, If the dimensions of the rectangle will generate...
3.Consider the following function where a is a positive constant exp(x / a) x<0 f(x) exp(-x/a) r >0 (a) Compute the area bounded by f(x) and the x-axis. Graph f(x) against x for a 2 and a 0.5. (b) Find the Fourier transform F(o) of f(x) (c) Graph F(o) against ω for the same two values of a mentioned (d)Explain what happens to f(x) and F(o) when a tends to zero. F(o) f(x)exp(-icox)dx 3.Consider the following function where a is...
Please answer the following questions with solution, thanks 4. Consider the function f(x) = 2x + 1, a) Find the ordered pair (4. f(4) on the function. b) Find the ordered pair on the inverse relation that corresponds to the ordered pair from part a). c) Find the domain and range of f. d) Find the domain and the range of the inverse relation off. e) Is the inverse relation a function? Explain. 5. Repeat question 4 for the function...
Graph of f Let f be the continuous function defined on (-1,8) whose graph, consisting of two line segments, is shown above. Let g and h be the functions defined by g(x) = h (2) = 5e-9 sin 2. -x +3 and (a) The function k is defined by k (x) = f(x) g(). Find k' (0) (b) The function m is defined by m (x) = 2007). Find m' (5). c) Find the value of x for -1 <...
Consider the generalized integrator function (2) discussed in class, defined by its proper- ties: | dr 8(x) = 1, Ve > 0, | dx 8(x) = 12+ = ſo if r* <0 11 if x* 20' dx 8(2 – c)f(x) = f(c), VER, where dc 8() is understood as a slight abuse of notation and f(x) in the last formula is a suitably well-behaved (at least bounded and continuous - and perhaps even smoother- in a neighborhood of x=c) function...
I only need c and d 9.9 1. Find a power series for the function, centered at c, and determine the interval of convergence, (a) f(x) = 1. 3-2 C=1 (b) g(x) = 2x-3 (c) h(x) = 2 + 2x - 3 (d) m(x) = *(1+r) (1 - )
2. Find the intervals on which the following function is continuous. tan r B( ) = V4-12 3. Find the derivatives of the following functions (a) f(z)= /5x +1 (b) gla) = (2r -3)(a2 +2) (c) y = In (x + Vx2 - 1) 4. Find the intervals on which the following function is decreasing. f(z) = 36x +3r2 - 2r 5. Evaluate the following integrals. r dr (a) sec2 tan (b) dar 3 (c) da 5x+1 1. Sketch the...