(b) Is the function h(u, v) = cos(u) + enu +sinh(u?) + vv+ enu , Where n is n=8. Is h is continuous? In case of yes then find the points of continuity. Explain briefly

Q: (a) Assume that g(x, y) is a function of the form g(x, y) = 0 if (x, y) = (0,0). (i) Show that g(x,…

A: As per the policy, we are allowed to answer only one question at a time. So, I am answering the…

Q: 4. Given J sec (1 – sinh-x) if r0 Discuss the continuity of f at r = 0 and r = 1. If discontinuous,…

A: Answer is mentioned below

Q: (a) Can [sin (x+y)]/(x+ y) be made continuous by suitably defining it at (0, 0)? (b) Can xy/(x² +y²)…

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Q: The function f(z) =e² is: u(x.y)=e*cos(y) o u(x,y) =e*sin(y) ¤ contiuous in СО discontiuous in CO

A:

Q: (b) Is the function h(u, v) = cos(u) + enu +sinh(u²)+ vv + enu , Where n=4. Is h is continuous? In…

A: (b) is the given function hu,v=cosu+enu+sinhu2+v+enu , where n=4 continuous? if yes then find the…

Q: r cos(y) + y(e² - 1) x + 0 f (x, y) = ry x = 0.

A:

Q: Let the function ƒ : R → R be given by 1- cos(x) if x + 0, f(x) := if x = 0. %3D 1 Prove that f is…

A: The solution is given as

Q: (a) Assume that g(x, y) is a function of the form g(x, y) {} 0 if (x, y) = (0,0). (i) Show that…

A:

Q: Find the Wronskian of the functions f(t) = et sin(t) and g(t) = et cos(t). NOTE: Your answer must be…

A:

Q: 30. Find the continuous function f(t) satisfying csin z for all r. 2+ f(t)dt = sin2015 /3

A: According to Leibnitz rule:

Q: (a) Assume that g(x, y) is a function of the form g(x, y) 0 if (x, y) = (0,0). (i) Show that g(x,…

A:

Q: By writing the ODEs in their normal form near the bifurcation point show that (a) ˙x = 1 + rx x…

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Q: Obtain an asymptotic expansion for I(z) = S e-zy°/2 cos y? dy, along [0, 0). as z → 00 -00

A: As per the question we have to find an asymptotic expression for the integral I(z). And we will do…

Q: Find and by implicit differentiation, and confirm that the - dy results obtained agree with those…

A: The solution is as follows

Q: Consider the function f(x, y) = V[ry[. Show that Taylor's expansion about the point (x, x) is not…

A: We know the Taylor series expansion of a function f(x, y) is given by, f(x,y)=f(a,b) +(x-a)…

Q: Find a potential function for F or determine that F is not conservative. F = (cos(z), 16y, -x…

A: The vector field given in the question is: F = <cos(z), 16y, -xsin(z)> Hence, F1 = cos(z), F2…

Q: Prove that the function f : R? → R, f(x, y) = sin(/x² +|sin y|) is uniformly continuous on R?.

A: The time interval between two waves is known as a Period whereas a function that repeats its values…

Q: Let F(x, y, z) = (sin(xy), cos(xy), sin(xyz)). What is the divergence of F at the point (T, 2, 0)?…

A: Given : F→x,y,z = sinxy, cosxy, sinxyz

Q: Find the Wronskian of the functions f(t) = et sin(t) and g(t) = et cos(t). NOTE: Your answer must be…

A:

Q: Define the map f : R² → R² as f(x, y) = (e" cos(y), æ²y + sin(y)) . (a) Show that f is…

A:

Q: Find the constants a, b e R so that the given functions are continuous on R. SO -22 + a, a sin ! +1…

A: A function f(x) is said to be continuous at a point  a if   limx→a-f(x)=limx→a+f(x) = f(a)

Q: Let f(2) = if z + 0 and f(:) = 0 if z = 0. Then %3D Select one: af is continuous at 0 fis not…

A: Option D is correct. See below for details.

Q: Use the Cauchy-Riemann Equations to show that f(z) = z Im(z) is only differentiable at z =0 and find…

A: Cauchy-Riemann Equations: Let f=u+iv be a complex valued function , then the Cauchy-Riemann…

Q: Show that the function f(z) = e-z",z # 0 and f(0)=0 is not analytic at z=0, although Cauchy-Riemann…

A:

Q: 4- Calculate the Laplacian of the following functions: (a) T e* sin4y cos 3z. (b) V = x° x^+3xz y-…

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Q: Discuss the continuity of the function. sin(z) ex + ey f(x, y, z) = continuous except at (0, 0, 0)…

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Q: Write the limit as a definite integral on the interval [a, b], where c; is any point in the ith…

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Q: (b)Consider the piecewise function g(z) = { (1+z)* – 1, if z >0 sin (4z), if z < 0. Discover whether…

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Q: Show that f is continuous at (0, 7) where a cos y + y(e" – 1) if r + 0 f(x, y) = ay if æ = 0.

A: In the given question we have to show that the given function f(x,y) is continuous at the point…

Q: The function f(z) =e² is: O contiuous in C discontiuous in C Ou(x,y) =e*cos(y) Ou(x,y)=e*sin(y)

A:

Q: Is the function h(u, v) = cos(u) + e™u + sinh(u²) + vv+ eu , Where n is second digit of your arid…

A: Use the properties that a term inside the square is supposed to no-negative number to get real…

Q: Consider the function f that is continuous on the interval [-5, 5] and for which 5 f(x)dx = 4.…

A:

Q: Q2. If ƒ = In(x² + y² +Z? ) then find the divergence of f also find its magnitude at (1,-2,3).

A: The given function is: f(x)=lnx2+y2+z2. Differentiate the given function with respect to x to obtain…

Q: Which of the following functions is continuous at (0, 0 )? f( x, y ) = In ( x² + y² ) ху Оb.f (x, у…

A: Which function is continue at point x and y=0

Q: (a) Show that the limit xżycos y lim (x.y)→(0,0) 2x+ +y² does not exist. (b) If u = x cos y+ ye»,…

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Q: Find the divergence of F(x, y, z) =(a -1 Y, y? + 1' 3xz2 + 2y ) at (2,0, – x COS

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Q: he tangent plane to the function f (x, y) = cosh x + cos(ny) + e*+1)y at the point (0, 1, f(0, 1))…

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Q: Is the function h(u, v) = cos(u) + emu +sinh(u?)+ vv + emu , Where n=6. Is h is continuous? In case…

A:

Q: Which of the following correctly states the First Fundamental Theorem of Calculus? (Read carefully,…

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Q: At what points (x, y, z) in space are the functions in continuous? h(x, y, z) = xy sin 1/z

A: Given function is  h(x, y, z) = xy sin 1z  We  have no additional conditions for x y part for any x…

Q: Discuss the continuity of the function. f(x, y, z) = xy sin z

A: Given- fx,y,z=xysinz To Discuss- The continuity of the above function. Concept Used- A function is…

Q: (a) Show that the limit x*ycosy lim (x.y)-(0,0) does not exist. (b) If u = x cos y+ye", wherex=s+2t…

A: The given function is f(x, y)=x2+y23 at point (0, 1) and direction u→=35, -45. The direction…

Q: Using an appropriate linearization, the local linear approximation of is f(x) = T+ cos r at 2.

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Q: Find the following limits proving whether they exist or do not exist 5y¹ cos²x x² + y² C) D) lim…

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Q: Consider the function f defined on [0, 1] such that / (0) = f(1) = 1.f(1/5) = {(3/5) - 2, and /(2/5)…

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Q: 3) Determine all points at which the following an functions are not Continuous: sin nur a) fe=で, )…

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Q: .a. Compute the divergence of the function (V. v) v = (r² cos²0) î + (r² sin²0)@ + (r sin® cosø)@

A: Note: Since you have asked multiple questions, we will solve the first question. Please resubmit the…

Q: 3. Evaluate the limit r(t +h) - r(t) lim h→0 h for r(t) = (t-1, sin(t), 4).

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Q: LET 2.3 + xy? if (x, y) # (0,0) f(x, y) = x² + 2y4 if (x, y) = (0,0). Show that f is not continuous…

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Q: Determine where h(x) = sin(x- Sx + 2) is continuous. %3D h is continuous on the interval [0, co). h…

A:

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.