Assume that f(z) = ez then Re(f(z)) and Im (f(z))are

Q: 1. If f(x) cos(t) dt, then f'(x) =

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Q: 'he function f: E → R is uniformly continuous if

A: We have to find the answer using the definition of uniform continuity.

Q: If f(x,y,z)=xe^{4y}\sin(6z), then the gradient is

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Q: For f(x) = e+cos(x), calculate f (0) by using the chain rule!

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Q: 1. Explain why / f'(t) dt = f(b) – f (a). ||

A: Refer to image below.

Q: Please help

A: Let,

Q: Sx, ifx 1 f(x) = Show that f is R- integrable.

A: R- integrable function

Q: Find f(4) if •f(x) b. a. t2 dt = x cos TTX. f(t) dt = x coS TX %3D

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Q: true false f(x) = R x −100 cos(t)dt and g(x) = R x π cos(t)dt are both antiderivatives of cos(x).

A: f(x) = R x −100 cos(t)dt and g(x) = R x π cos(t)dt are both anti derivatives of cos(x).

Q: Prove that = va² – x* if y =(f)sin~+ () + (9)v&* - x²

A: Differentiation wrt x

Q: If g(x) = ªſ*'[e'− In(2t+1)]dt, find g ''(x) . - dx -2 4 A + (2x + 1)2 Be-In(2x+1) 2 C (2x + 1)² 4 D…

A: Given that,      gx=ddx∫-2xet-ln2t+1dt

Q: If g(x) == [e'-In(2t+1)]dt, find g''(x) . dx A ex-In(2x+1) 4 B (2x+1)² 4 (2x + 1)² 2 D (2x + 1)²

A: Here given that: g(x)=ddx∫-1xet-ln(2t-1)dt Using the Fundamental Theorem of Calculus: g(x)=ex-ln…

Q: Prove 8xyz < (x + y)(y + z)(x + z) for every x, y, z E [0, +∞[.

A: We have to prove given identity: Concept:

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

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Q: | f(t) dt = x*e* e + a

A: This question is based on integration.

Q: Find the linearization of the function f (x) = x' at x = 1. a ab Va |a| sin (a) 7 х-6 L (x) Using…

A: Given a function,

Q: If f(x) • cos ( z ) t'dt then f'(x) =

A: We can find the answer as below

Q: Verify Young's Theorem y? x2 z = In(2x + y) – + e(x+2y) + - y

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

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Q: Suppose F(x,y)=sin²(xy +e"), where x=u² +v and y = In(u² +v). Find the . ƏF ¸ ÔF value of when u =1…

A: The given function is: F(x,y)=sin2xy+eywhere:x=u2+v         and         y=lnu2+v

Q: Let f (x,y) =In Then f „(1, – 1) =... 3x²+ 4y3

A: This is a problem of partial.

Q: 1 Find F'(0) given that F(x) = dt. In(t + 1) 2

A: F(x)=∫2x11ln(t+1)dt

Q: If f(x) = , dt, then f'(x) = %3D %3D t4 +1 1 Select one: a. e-4z + 1 -e b. x4 + 1 -e С. e-4z +1 e d.…

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Q: If A(x)= f(t)dt is increasing on [0,10], then f(x) must be increasing on [0,10].

A: Given,A(x)=∫0x f(t) dt

Q: If F (x) = (t2) dt , then F' (4) = cos 0,

A: DUIS rule is used

Q: If f(x) I (t° + 2t + 6) dt 0. then %3D = (x), ,f

A: The function needs to be integrated first and then to the subsequent function we will be double…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. h(x)= ].…

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Q: e If F(x) = | e dt, find F(1) and F'(x). ez

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Q: Find f(t). s(s + 1).

A: L-1[F(s−a)]=eatf(t) From first shifting property, L{e^(at)*F(t)} = f(s-a)…

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: a) If F(x) = | 1 dt, then F'(x) = t 14 1 b) If F(2) = dt, hen F'(2) = 1 c) If F(x) = / dt, then…

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

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Q: If f(x) = t°dt then = (x),f

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Q: If F(x)= J. x) = [", "+!dt then F'(x) dt , then F'(x)= /3 sint

A: If Fx=∫π3xt2+1sintdt, then evaluate the value of F'x.

Q: (b) Prove that sint -dt > 0 t+1 for all a > 0.

A: Given:- ∫0x sintt+1dt &gt;0

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 total differential df of f (x, y) = (x² + y²) 3/2.

A:

Q: Find the linearization of the function f (x)= x³ at x = 1. qb |a| sin (a) L (x) = Using this…

A: Given, fx=x5 We know that, If we have a differentiable function f defined near "a" the linearization…

Q: Verify Young's Theorem S. f(x, y) = = e(2x+y) In(xy)

A:

Q: d Use the chain rule to calculate f(x) if f(x) In (1+ tº) dt. dx, 0. f(x) =

A: let's use chain rule and find derivative of integral.

Q: If e**У- ху, then dx x(1- y) A Ax- 1) Ax - 1) B x(y- 1) (1- x) x(y- 1) x(y- 1) (D Ax - 1)

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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: find ∇f at the given point. ƒ(x, y, z) = x2 + y2 - 2z2 + z ln x, (1, 1, 1)

A: Given function is fx,y,z=x2+y2-2z2+zlnx and point=1,1,1

Q: (ii)If y=(x+Jx* +1. prove that y'= Vx +1

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Q: The function e is an integrating factor for the ODE y' – 2xy = x7 - True False

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Q: If F(x)=[ cos(t² +1)dt , calculate using the fundamental theorem of calculus derived version.

A: Given : F(x)=∫-xxcos(t2+1)dt Aim: to calculate using the fundamental theorem of calculus ,the…

Q: if u(x) = x^2+1 and f(u) = u^2, then  df/dx = (2u)(2x) = 2((x^2)+1)(2x) you can check the…

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Q: Let W=x*yz.compute the differential dw.

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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.