Basic Math question and answers for August 03, 2023
- Q Given: f (x) = (x − 2)/(x^2 − x +1)^2 a) Find the intervalswhere f(x) is increasing, and decreasing b) Find the intervalswhere f(x) is concave up, and concave down...
- Q Find the exact value under the given conditions1) tanx=-7/24, x lies in quadrant 2, cos(y)= 3/4, y lies inquadrant 1Find: sin(x+y), cos(x+y), tan(x+y)2) cos(x)=21/29 x in quadrant 4, sin(y)=-5/12, y...
- Q Exactly one of the following statements is true. Which one?Select one:a. Every convergent sequence is monotonic.b. Every Cauchy sequence is monotonic.c. Every Cauchy sequence is bounded.d. None of the other...
- Q Consider a wire of length 4 ft that is cut into two pieces. Onepieces form a radius for circle and other forms a square of side x.1) choose x to...
- Q Let S be the solid bounded by the surfaces z=2sqrt(x^2 + y^2)and z=2. Suppose that thedensity of S at (x,y,z) is equal to z.Set up an integral for the mass...
- Q Find the maximum and minimum values of the functionf(x,y,z)=3x−y−3z subject to the constraints x^2+2z^2=49 andx+y−z=9. Maximum value is Maximum value is  , occuring at( ,  , ). Minimum value is  , occuring at...
- Q Find the positive numbers x, y and z whose sum is 100 such thatx^r y^s z^t is a maximum, where r, s and t are constants.
- Q Find the vertical asymptotes (if any) of the graph of thefunction. (Use n as an arbitrary integer if necessary. Ifan answer does not exist, enter DNE.)h(x) =x2 − 9x3 +...
- Q The amount of carbon-14 present in a tree is given by theformula C(t)=C0e−.00012t, where C0is the amount of carbon-14 present in it at the time of its deathand t is...
- Q On a sketch of y=ln(x), represent the left Riemann sum with n=2approximating ∫3to2 ln (x)dx.Write out the terms of the sum, but do not evaluate it:Sum = ?? + ??On...
- Q series from n=1 to infinity of (4n) / [ (3n^3/2) +7n -9]. theanswer should include if its converging or diverging by whichmethod
- Q f ''(x) = −2 + 24x − 12x^2, f(0) = 7, f '(0) = 12
- Q Se estima que la población de la tierra en el 1500 fue de 100millones de personas. En 1990 la población mundial se estimó en2600 millones. Asumiendo que la tasa de...
- Q Cuando un rayo de luz pasa a través de una sustanciatransparente, el grado con que la intensidad, I(h), disminuye esproporcional a la misma intensidad I(h) donde h representa elespesor del...
- Q A particle is moving according to the given datav(t)=t^2 - sqrt(t), x(0) = 0, 0 ≤ t ≤ 4.• Find x(t), the position of the particle at time t.• For...
- Q Prove that one of the diagonals of a kite bisects two of theangles of the kite. What about the other diagonal — must it also bean angle bisector? Explain your...
- Q write a power series for f(x)=5/(x+3)c=2
- Q Suppose that human pregnancies have an average duration of 270days and standard deviation of 14 days. Find the probability that apregnancy lasts for(a) Less than 270 days(b) Less than 263...
- Q Compute the unit binormal vector and torsion of the curve: ?⃗⃗(?) = 〈12?, 5cos ?, 5 sin ?〉
- Q The population of the earth in the 1500s was estimated to be 100 million people. In 1990 the world population was estimated at 2,600 million. Assuming that the growth rate...
- Q Find dy/dx by implicit differentiation.11. ycosx=x^2+y^213. sqrt(x+y)=x^4+y^415. tan(x/y)=x+y17. sqrt(xy)=1+(x^2)*(y)19. sin(xy) = cos(x+y)
- Q There are several interpretations for the derivatives, both froma geometric and algebraic point of view. Polynomial functions arethe simplest to perform the derivation. Knowing how to calculatethem is fundamental for...
- Q How do I find the area between the following two polarcurves.r = 2cos(theta)r= sin(theta) + cos(theta)
- Q Estimate the area between the graph of f(x) = x3 − 12x and thex-axis over the interval [−2, 1] using n = 6 rectangles and rightendpoints. Draw thecorresponding rectangles as...
- Q Find the derivative of the parametric curve x = 6t - t^2, y =lnt where t > 0A. Find all values of t where the tangent line is horizontal. Afteryou...
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