ition of cont s continuous at the given point. a). f(x) = , a = 3 Use the 2z– -32

Q: 2. (a) Use algebra to verify that (1+ (x – 1) (b) Differentiate arctan(x+1) – arctan(x- vital thing…

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Q: TOTAL.40IMark uestion 5 a. Let f (x) = sin(ax + b) and let g (x) = cos(ax + b) where a and b are…

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Q: 4) Let F(x, y) = yi+xj. a) Show that F is conservative and find a function f such that F = = Vf. b)…

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Q: cos (Vx)= 4x- a, Co,) 2

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Q: (4)using the relation F= Vn show that J1(x) cos x %3D

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Q: a) Use the definition of the hyperbolic functions to prove that 2cosh?(x)–1=cosh(2x). 1%3D

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Q: 1. Consider the function f given by f(x)=√ √Int²-1dt 1 Compute the length of the curve y=f(x) from…

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Q: (2) Find a smooth curve a in GL(2, R) passing through the identity such that a'(0) 1 0 Justify your…

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Q: (a) Use the Product Rule twice to prove that if f , g , and hare differentiable, then (fgh)'   =f'gh…

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Q: 22.5 Integrate the following function use two, three and four points Gauss Quadrature [xe**dx

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Q: Determine Taylor's formula of order 1 and center a = (0, 0) of f(x)=ex1sin(x2).

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Q: Prove that the Lagrange's fomula can be put in the form ø (x) f (x,) (x- x,) ø' (x,) P„(x) = £ %3D |…

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Q: 6. Let f(r) = -a cosr. With po = -1 and p1 = 0, find p3; %3D

A: f(x)=-x3-cosxp0=-1p1=0To find:p3=??

Q: Using an appropriate linearization, the local linear approximation of f(x)%3D+ cos r at is 2.

A: To determine the linear approximation of the function.

Q: ldéntities will prove useful in achie Exercise 12. Show that E, (T: – ¤) = 0 %3D | E (*: – µ)² = E…

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Q: A. Find F(s) for f(t) = sin? 4t LIcing cocopd chifti ng theorem find Fle) whore f(+) -4t ain 2+

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Q: Prove that the Lagrange's fomula can be put in the form ø (x) f (x,) (x- x,) ø' (x,) n P„(x) = Ë r =…

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Q: π 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x = - to x = 4 4 (A)…

A: See the details solution in below

Q: (a) Find a harmonic function u on the upper half-plane that has the following boundary values. (1…

A: Detailed explanation mentioned below

Q: F(x, y, z) = e-* sin y i+ e-Y sin z j +e- sin x k

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Q: 6- What is the arclength of the function y = 7x + 2 on the interval [2,6]? a) O /2 90406 b) O 20 c)…

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Q: 1-cosx 4x2 k , x =0 Find k so that (x) = is continuous at x=0 A 2/5 В) 1/8 c) 1/2 D) 3/4

A: As per bartleby guidelines we only give first question answer.

Q: 1. Prove: a. S csch x = In|+ c b. S sech x = 2 Arctan(e*) + c

A: *As per the guidelines, only the first question is supposed to be solved. Please repost remaining…

Q: 2-) [l,e] Find the area ot the reslon under +the f Cx) = Inx on the range

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Q: Let L(z) be the linearization of f(x) = sin x + 1 at the point x = . Find L(1/2). O -1 pi/2-1…

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Q: let FCXye+ Siny) f+ (ex+ cos y for pai-) Shoul Hhat F is coserative Vutor Funtion 6) Find a funtion…

A: F is a conservative function iff its curl is 0 that is determined as. Here F is determined to be a…

Q: Find the extrema of the given function f(x, y) = 6 cos(x² - y²) subject to x² + y? = 1. (Use…

A: Given f(x,y)=6cosx2-y2 subject to x2+y2=1

Q: 3. Find the singular points of the following functions and discribe the types of singularities 1-…

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Q: Using an appropriate linearization, the local linear approximation of f() = T+ cos z at COS I is -…

A: Use linear approximation

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Q: H.W: what is L of f(t)=sinhat а ANS: (s2-a?)

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Q: 10. Find all the values of a in the interval [0, 27] such that f (a,=) - fxx (a,=) = 0 for f(x,y) =…

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Q: Find div F and curl F if F(x, y, z) = 7evi-4 cos yj+ 10 sin² z k. div F= curl F

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Q: Show all steps to verify that fry = fyx given f(x, y) = cos(2x) – x²e5y + 3y²

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Q: Prove that arctan x + arctan y = arctan(x + y) / (1 − xy),  xy ≠ 1.                   Use the…

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Q: A. Ifw= sin(x+bt)+cos(2x+ 2bt) . Prove that ôx? B. If f = x*y* + 2y sinx + x² lny then show that fxy…

A: A)

Q: QI If f(2) s analy tic function for all 2 Prove tha t dy

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Q: π 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x=- to x=—. 4 4 (A)…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

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

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Q: (f) Prove that f(x) = 1.1z + cos(z) has no more than one root. (Note: It is not enough to have…

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Q: B) Use Green's Theorem to evaluate /F-dr, where C is a triangle from (0,0) to (1,0) to (0,3) to…

A: We will use Greens theorem here

Q: in the rectangular ax+by+c = 0 is coordina te system. Accordingly, show the expression F that is a…

A: Given: ax+by+c=0; in the rectangular coordinate systemis a  straight…

Q: HiW Q Prove that : tanhclax) = x-! %3D x2+1

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Q: Is there a value of b that will make f (x) = {cos a, r>0 differentiable at x = 0? Upload Choose a…

A: Explained below

Q: Q5: Find W,e if W = f(x,y), xr cos6 and y =r sino, then prove that r Wre =-yf + xfy+ xy(fyy-fex) +…

A: The given problem is to find the double partial derivative of the given multi variable function and…

Q: (a) Show that y = x* is concave upwards at the origin and y= e* is everywhere concave upwards.

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Q: Let f (x) = In (x?) find the equati on oE the line tangent to the graphof f at (3, In(9)) (2) Find…

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