´t+2, t² +1, 01.

Q: Given f(x, y) = x²y – 2xy + x² – 2x + y² – y. (a) Find the critical points of f. (b) Use the Second…

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Q: f(x) is a positive continuous function on R what does the function F(x)= | f(t) dt a represent (for…

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Q: iven F(x) = L- (1 – /1– (1+1)² ) dt valuate F(0) and F'(/2) using the First Fundamental Theorem of…

A: We have to find out

Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y = 2rsine

A: Here, the total derivative rule used is: z=f(x,y)=x2y2 & x=2rcos θ , y=2rsin θ

Q: Find the linearization of the function f (x) = x at a = 1. a Va lal sin (a) L (1) Using this…

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Q: 11) Consider F(x) = S*sec t tan t dt a) Integrate to find F as a function of x b) Demonstrate the…

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Q: A continuous P&I= {ac Find V-V. 6CX-X2) C D F x has the pdf UCXCI F(x) other

A: Given PDF is P(X) = 6(x-x2),0<X<10,otherwise

Q: 2) Find a value of c for which f (x) is a pdf on the f(x) = cx + x², [0. 1]

A: Introduction ∫-∞∞fxdx=1 The total area under the curve fx of pdf is 1.

Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y=2rsinė

A: this is a problem of differential. Based on the general formula and concepts we will answer the…

Q: II. Let F(x)= ecosh z √x+1 1. Find F(0). 2. Find F'(x). sin(1-t) dt.

A: Let Fx=∫x+1cosh x sin1-t dt.1 To find F0.2 To find F'x.

Q: u(x) = x° - 1 x = 1 at Select the correct response: O Continuous Discontinuous

A: As per guidelines we can solve only one question at a time, if you need more answer kindly repost…

Q: 4. Let I = [0, 1] and let f : I → R be continuous. Suppose that | f(t)dt = f(t)dt, x E I. Prove that…

A: f(x)=  0 for all x in [0, 1]

Q: Find the linearization of the function f (x) = x at x = 1. a lal sin (a) L (x) Using this…

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Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2]

A: Consider the given function fx,y=3x2-2xy+y2-8y First, find the partial derivatives of the function…

Q: (a) express dw/ dt as a function of t, both by usingthe Chain Rule and by expressing w in terms of t…

A: Consider the following equation: w=x2+y2 Substitute x=cost+sint and y=cost-sint in the above…

Q: f(2) = | : t2 – 1 dt 1+ cos² (t) At what value of ¤| does the local max of f(x) occur?

A: Given that a function f(x) and we find value of x does the local maxima of f(x) occurred. We know…

Q: find ∇f at the given point. ƒ(x, y, z) = 2z3 - 3(x2 + y2)z + tan-1 xz, (1, 1, 1)

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Q: Find the linearization L(x) of f(x) = cot(x) at x = π/4.

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Q: Let g(x, y) = x4 + y² – 4x³ + 5x – 6y+3. Show that g(x,y) continuous (actually at least aC')…

A: Recall [ Implicit Function Theorem ]

Q: * (0,0) is not continuous if (x, y) Q.3 ( 3+3+4) (a) Prove that the function f(x,y) = {2x+y (i if…

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Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2].

A: We have f(x, y)=3x2-2xy+y2-8y find critical points ∂f∂x=6x-2y=0 ... (1)∂f∂y=-2x+2y-8=0  ...(2)solve…

Q: 18. Let ()- xy6 x4 + y8 ' x+ 0, f(0) = 0. %3D (a) Find all the directional derivatives of f at 0.…

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Q: Let g(x) = kf(x) for all x E/= {x: asxsb}. Show that Jglx)dx = kJ f(x)dx if k<0.

A: To prove the above result we use the definition of lower and upper Riemann integrals. For the proof…

Q: Recall the chain rule from differential calculus: f (g (æ)) = f' (9 (æ)) · g' (æ). d dx Find de tan…

A: We have to find

Q: Find the linearization of the function f (x) = x° 26 at æ = 1. a vā |a| sin (a) L (x) = Using this…

A: I am going to solve the given problem by using some calculus to get the required result.

Q: Ag(2) is a continuous function on :Select one .a Ɔ C-{z = x + iy : y = 0,x 0}. .C C- {z = x + iy :…

A: We have to find the area on which arg z is continuous

Q: (b)Assume that f(x) is a function of the form -x-1; when -T < x <0 f(r) = when 0 <r < T Prove…

A: For the solution of the problem follow the next step.

Q: Find the linearization L(x) of f(x) = cot x at x = 4

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Q: Q2 (A) At what points f(x, y, z) in which the function f(x, y, z) = continuous? is

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Q: - Find the total differential df of f (x, y) = (x² + y²) 3/2.

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Q: III. Let g be defined by the equation g(x) = dt t²-1 Show that g'(x) = secx.

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Q: 6. let h be the function defines by h(x) = 2e***dt, Find h'(2) %3D

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

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: x-1, -1 sx< 0 0<x <1 x = 1 1<x< 2 2 <x<3 2r, f(x) = 1, -2r + 4, 0, Is f(x) is continuous at x = 1…

A: Given: f(x)=x2−1,−1≤x&lt;02x,0&lt;x&lt;11,x=1−2x+4,1&lt;x&lt;20,2&lt;x&lt;3 A function f(x) is…

Q: (d) The function x²+y? Vx2+y? (x, y) # (0,0) f(x, y) (x, y) = (0,0) is continuous at (0,0).

A: Note: according to Bartleby policy we are allowed to write only one question please post remaining…

Q: Q1. (a) Find the points (x ,y, z) in space, where the function f(x, y,z) = /x² +y² -1 Is continuous.

A: Given :- The points x,y,z in space , where the function f x,y,z = x2 +y2 -1 is continuous.

Q: Suppose that f(a) = f(b) = 0 and the second derivatives of f exist on the closed interval [a, b].…

A: Prove that ∫abx-ax-bf"xdx=2∫abfxdx.

Q: 3. Let f(x)= :/ arcsin(t) dt and g(x)= / arccos(t) dt. 0. 0. I f'(x) g' (x) dx =? 4 - T (a) 2 - T…

A: Given Applying derivative with respect to x: Similarly:

Q: Q: Which c.d.f. F is of X is continuous at x=0?

A: If F(0) = F(0-) then F(x) is said to be continuous at x = 0

Q: e-(z-1)2-y 1 (r, y) # (1,0) If f(r, y) = (I-1)2+y (r, y) = (1,0) %3D is continuous at (1,0), what is…

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Q: A function y(t) satisfies th

A: Given, the differential equation                       dydt=-y4-3y3+4y2

Q: 2. Let f(x) = (x + 1)( arctan(1 – 2x) + /. f(t) dt x2 Which of the following statements are correct?…

A: Some properties of derivative  Let us consider  and if the limit on substituting x=a  as…

Q: 1. Find if the function is continuous in the given points (x, y) = (0,0) (x, y) = (0,0) x + y = 0 x…

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Q: Using the second fundamental theorem of calculus and chain rule, compute t dt. t+1 dx 2x

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Q: 32 2 f is continuous and | f(t) dt = 6, find the integral / t* f(t) dt.

A: Given problem:-

Q: w(x) = |x + 1| m at x = 1 Select the correct response: Continuous Continuous

A: For continuous function LHL is equal to RHL and function values same

Q: (d) The function x²+y? Vx²+y? (x, y) ± (0,0) f(x, y) = (x, y) = (0,0) is continuous at (0,0).

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Assume x and y are functions of t. Evaluate dy / dt for 3xy - 6x + 4y 3 = -80, with the

A: