3 4. Find the convolution of f(t)={2' -t, 0 6

Q: The equations of the vertical asymptotes of the function with rule f (0) = are: 1+ cos 0 e = 3rk…

A: Take denominator of f is equal to zero.

Q: Solve the DEQ given the initial condition (-2,5). Graph it on the slope field. 1 + Let g(x.y)=dy/dx…

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Q: 22 dt at x = 4. ind the linearization of f(x) = 7 - 4 +t

A: Consider the given function fx=7-∫7x+3224+tdt

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A: The given function is,  F(x,y,z)=x2y2-xz2 We have to find,  a) ∇F b) Equation of the tangent plane…

Q: 15.4.59 Assume that F(x.y,z(x,y))3D 0 implicitly defines z as a for xyz + 8x + - 4z = 0. dz

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Q: the Following is divergent

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Q: 1 Q9: Let f(x) = cosx x + 3 then find all critical points. 2 -

A: A critical number C is a number in the domain of 'f' for which eitherf'c=0 or f'cdoes not exists.…

Q: Find L(x). 2y x 3t %3D y + a' = 3e-t x (0) = y (0) = 0 3s2 L (x) = - (s+1)(s-2)(s²+1) 3(s-1) L (x) =…

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Q: If f (x) is an invertible, differentiable function with tangent line y = 4 x + 7 at the point (0, 7)…

A: we have to swap variable for finding the inverse function

Q: 2. Show that if zo is an isolated singularity of f(z) that is not remov- able, then zo is an…

A: We have to show if z0 is an isolated singularity of f(z) that is not removable, then z0 is an…

Q: 4.) Suppose X has moment generating function MX(t) = 0.3e−t + 0.1 + 0.1et + 0.2e2t + 0.3e3t. What is…

A: It is an important part of statistics. It is widely used.

Q: or what values of the constant m does the Second Derivative Test guarantee hat f(x,y) = -2x2 + mxy –…

A: Solve by saddle point method

Q: X1, ., Xn are idd. find the MLE and cramer rao lower bound for unbiased estimator for theta. f (x |…

A: Given  fxθ=θ              when x=-11-θ2θx     for x=0, 1, 2, ....

Q: Consider the function 0. f(t)3D- t = 0 if if t # 0

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Q: 11. Find the linear approximation to given function at indicated point (Баллов: 2) x2 z = 3 + +, Po…

A: Topic:- linear approximation

Q: 6. Consider the function f(x, y) = cot ¹(1+x) — 2e¹+³y If x = s²-t² and y = 3t+tan(1-s), use the…

A: Let's evaluate given partial derivative.

Q: 4. Determine all the critical points for the function f(t) = Vt² (2t + 1)

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Q: (8) Suppose f(x, y) = -x + y², x = s² +t°, y = 2s – 3t. Compute f, when s = 1 and t =-1. %3D

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Q: [2.73 Find a general Solution of following monhomogeneous limear 1ogeneous linear ODE g+ +1+#)は = e…

A: non-homogeneous differential equations

Q: frod ll Critical points on the fcx) = x² Jq-x² 2. curve f(x)

A: Solution:- Critical point:- critical points are point where the function f(x) is defined and its…

Q: 23. Given that f(0) = v2 cos (e-), the minimum value of o1+ v2 C. %3D COS D.-1 A. V2-1. B.2N2

A: Since you have posted multiple question in this question so I have solved first question as per our…

Q: (3) A study on optimizing revenue from a website considered dividing cus- tomers into two groups…

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

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Q: 1. Find the critical points of f (x,y) = 8y³ + x³ – 6xy and use the second derivative test to…

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Q: Xn Xn=3-(-1)" xn = cos (¹₂) √1+n² Xn= 27-5 Xn=¹ where (yn) is bounded 4 lim inf(x) lim sup(x₂)

A: We know the fct that for every  bounded  sequence  limsup(xn) and  liminf(xn) exists finitely. since…

Q: 2. Find the linearization of the function f(x, y) = In(x³y®) at the point (xo, yo) (4, 3). Leave all…

A: Consider the following function: fx,y=lnx3y6 fxx,y=ddxlnx3y6=1x3y6×3x2y6=3x…

Q: 5 of 9 > Let f(x, y, z) = 5x³ · y³ + z². Find the maximum value M for the directional derivative at…

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Q: Verify Young's Theorem In(2x + y) y2 x2 + + e(x+2y)

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Q: 1 Verify Eular's theorem for z=- =(x²+xy+y*)' x²+xy+y² 2

A: The expression z=1x2+xy+y2=x2+xy+y2-1. We have to verify the Euler's Theorem.

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: 2. Suppose that z = f (x, y) and both x and y are functions of a single variable t such that dy t2 –…

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Q: 3. Find the Absolute Minimum and Absolute Maximum of f(x,y)=xy subject to 2x² +8y² =144 Fully…

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Q: Chapter 7, Section 7.7, Question 012 Use the inequalities JEM| = ƒ (x) dx 24n2 (b - a) K2 |Er| = f…

A: Given that the integral is ∫0414x+1dx. a) It is required to find the upper bounds on error obtained…

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

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Q: 7. The function (x, y)= (2x* + y* )exp + xy' is homogenous in x and y of degree

A: .Given,f(x,y) = (2x4+y4) ey2x +x y3Put y= xSo we get,f(x,x)= (2x4+x4) ex2x +x x3 f(x,x)= (3x4) e0.5…

Q: 39. (a) Show that 1 1 > 0 2x V1+x² for x > 1. (b) Use your result in (a) to show that 1 dx 1+x is…

A: The compleet solutions are geven below

Q: 3.2 Let f(x) = Approximate the integral x4 x L f(x) dx using the Trapezoidal rule with n = 4. -2

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Q: Solve the DEQ given the initial condition (4,-2). Graph it on the slope field. 10 9 1 8- Let…

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Q: Consider the IVP S2(t) = -1+cos(t + x(t)) cos(t + x(t)) x(0) = 0. Show that the ODE is exact and…

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Q: 8. Find and classify all the critical points of f(x, y) = 4x y+ 2xy - 6xy.

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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: 1, Differentiate the function. (1) f(x)= /32 (2) f(x)= (x°+10) 5 (3) f(x)= 2.x - V х (4) f(x)=…

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Q: 3. Find upper bound for error of linearization of the following function at given point Po(1,2), 4.…

A: We can solve this by using partial derivative formula

Q: Suppose that r1 and r2 are roots of ar2 + br + c = 0 and that r1 ≠ r2; then exp(r1t) and exp(r2t)…

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Q: F.M: 15 1. Use second derivative test to classify each of the given critical numbers as a relative…

A: 1. A) f(x) = e-x(x² - 3x + 1)  So, f'(x) = e-x(2x - 3) - e-x(x² - 3x + 1) So, f'(x) = e-x(2x - 3 -…

Q: 1) fl2) - 3 2) Sla)-- 2) sle)=- -3 5 A) s'ls)- - 4 17 3" 3 A) Yes B) No B) s "4)-+ 8 B) s (1)– 3. C)…

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Q: 1 If f(x,y) =- and (x, y) changes from (3, 4) to (3.2, 3.9), x²+y² compare the values of dz and Az.…

A: