2. Find the absolute maximum and absolute minimum values of fon the given interval. f(t) = t – Ve, [-1, 3]

Q: B If f(x) has a local minimum at ra, then which of the following must be true? O f'(a) > 0, f"(a) 0…

A: We have to find the correct option.

Q: - Determine the largest interval in which the unique solution of (t – 3)y +tan t y =t, y(n) =0 is…

A:

Q: 1. Find where f(x, y) = 4x² + 8y? – 4x – 8y +5 has absolute extreme values over the square with…

A: To calculate the extreme values of f(x,y)bounded by the square, the following calculations need to…

Q: Find the absolute maximum and absolute minimumvalues of  f on the given interval.

A: Given equation is Differentiating both sides, we get Now, we will wind critical points of f(t) in…

Q: Assume that after  months, butterflies’ populace  in 1000 is calculated as: f(w) = 12w + cos(16w) +…

A:

Q: 18.7. Let f(z) = (e + e-2)/2. Evaluate f(2) -dz, where y is any %3D simple closed curve enclosing 0.

A:

Q: Suppose that T is to be found from the formula T=y( e*+ e-X), where x and y are found to be In 5 and…

A: GivenT = y(ex + e-x)

Q: 1. A) Find the linearization of the function at the given point. f (x, y) = 2 + x In (4 – xy), at…

A: (NOTE- These are two completely different questions, only required to do the first one. Please post…

Q: For function f(x,y) to have minimum value at (a,b) value is? 1) rt - s>0 and r0 and r>0 3) rt - s?0…

A: For a function fx,y to have minimum value at a,b, which of the given condition is true? 1)…

Q: Suppose that Tis to be found from the formula T=x(ey + e -), where x and y are found to be 2 and In…

A: Suppose that T is to be found from the formulaT=xey+e-y where x and y are found to be 2 and ln2 with…

Q: Sketch a graph of each of the following functions that captures the limiting behaviour as t → ∞ and…

A: Note:- As per our guidelines, we'll answer the first three sub parts since exact three were not…

Q: 10 a- Let X1, X2, ..,Xn~N(0,0) and T Find %3D X2 E (T),Var (T)

A:

Q: 5. Determine a function v(r, 0, ø) with Av = 0 _in B2 \ B1 satisfying the boundary conditions v(1,0,…

A: Use the cylindrical coordinates to determine the value of r. Now use the boundary conditions to…

Q: Find the Wronskian for the set of functions {e¬*, xe¯×, (x + 1)e-*}.

A:

Q: Determine the largest t-interval on which we can guarantee the existence of a solution of the IVP:…

A: To determine the largest t-interval on which we can guarantee the existence of a solution of the…

Q: 16. Let h(x, y) = xy – 2x². Find the minimum and maximum values of h on the rectangle where 0 < x <…

A:

Q: 18. Find the absolute maximum and absolute minimum values for the function f (x,y) = e-**-y* (x² +…

A:

Q: Let xo E (0, o0) be the value ofx E (0, 0o) that minimizes the function f: (0, co)R defined by f(x)…

A: The given function is fx=x2+x-2. the graph of the given function is, Clearly it is not defined at x…

Q: 3. Find the interval on which the curve of y= 2 1+3t+t² dt is concave up.

A: Second derivative is positive.

Q: If Σ α An diverges then E ca can diverges only if c > 0 only if c < 0 only if c+ 0 for any real…

A: Given, ∑an diverges then find for which values of c, ∑can diverges.

Q: 2. Show that g(x)= *** has a unique fixed point in [0,1] and find an approximation to the point that…

A:

Q: Find for x = x(t) defined implicitly by 25+25 x In(t) = e25xt Also evaluate dt at (t, x) = (1,1).

A: Given,25 + 25xlnt = e25xtTaking 'log' with base 'e' on both side, we getln25 + 25xlnt = lne25xtln25…

Q: Find solution of an equation X f(x) 1.0000 1 1.25 0.8000 1.50 0.6667 1.75 0.5714 2.0 0.5000 a. Using…

A:

Q: Find the absolute maximum and absolute minimumvalues of  f on the given interval.

A:

Q: ii. Establish the stability estimate for the solution of the problem "() - by(le) + ay(t) + f(4) on…

A: Given that , y''t=byt+ayt+fty''t=abyt+ft Therefore the differential equation , y''t-ab yt-ft=0 The…

Q: (4) Let f(x, y) = e-y. Find the linearization of f at an appropriate point and use it to…

A:

Q: 1 Let H(s) Using convolution to find h(t) s2 (s-a)

A: Inverse Laplace transferom

Q: 5) Construct a linear approximation of the function f(x ) = lacX+s) about the point x,= 1. Compare…

A: Tangent line approximation or linear approximation is very significant in differential calculus.…

Q: Suppose there is no known formula for g(x), but we know that g(2) = -1 and d (z) = V2 +5 for all x.…

A:

Q: 5 The function f (x, y) =| x² cos² is homogenous in x and y of degree,

A:

Q: Given f(x)= x' – rx + k where r E r > 0 and r # 1, and k to be any constant. Prove tha if 0 1, fhas…

A: The given function: Where and k to be any constant. To prove that: If 0&lt;r&lt;1, f has a…

Q: Find the absolute maximum and minimum values off on D, where f(x, y) = x – 2xy+2y and D={(x,…

A:

Q: 4.2) Suppose you wanted to find the absolute extrema of f(x, y) = ax² + bxy+cy? + dx + ey on the…

A: The given function is, fx,y=ax2+bxy+cy2+dx+ey We have one critical point on the rectangle,…

Q: 8. Let f(x, y) = cos(y – x) and r(t) = (e', e2t). Find if (r(t)) at t = ln(3).

A: The solution is given as

Q: Suppose fn → f and the functions fn all satisfy the Lipschit condition |fn(x) – fn(y)| < Mx – y| for…

A:

Q: Find the minimum and maximum of A over a particular interval [0, 6]. A(x) f(t) dt The graph of y =…

A:

Q: 27. Find the length of the curve Vcos 2t dt y = from x = 0 to x = "/4.

A: The given curve is We know that by Second Fundamental theorem of calculus ,if F(x) is continuous on…

Q: Find T(t), N(t), a-, and a, at the given time t for the space curve r(t)- Function Time r(t) = 4- j…

A:

Q: 5 The function f(x, y) = | x' cos is homogenous inx and y of degree

A: Given that: f(x, y)=x2cos2yx-y2+x3y

Q: Find the absolute minimum and absolute maximum values off on the given interval. f(t)=t√ 25-t²,…

A:

Q: Given a function f(x, y) = x° + y° + 3x² – 18y + 81y + 5 - The function has four critical points in…

A: Consider the given function as fx,y=x3+y3+3x2-18y2+81y+5

Q: 5) a) Compute Ko for the function f0=V+X by using the de finition of the deniratire, b) Find the…

A:

Q: 9. Find the orthogonal trajectories to the following families of curves: x = ke¯v, where k is a…

A:

Q: Which of the following functions has a maximum y value of 4 Oy= 4cos x y= cos 4x Oy= cos x + 4 Oy=…

A:

Q: The function f(x, y) = x² + 4y2- 2x + 8y-1 has a local minimum at the point (-1, 1). Select one: O…

A: We will use first order derivative to find critical point.  If given point is critical point, then…

Q: 1. Use the Gauss forward formula with xo = 2.0,h = 0.15, n = 7 to find an estimate for f(2.5) if %3D…

A: Given: fx=xlnx. x0=2.0, h=0.15, n=7.   We can solve this by using Gauss forward formula

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.