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Q: The slope of the tangent to the graph of g(x)=(6x +1)° at the point (0, 1) %3D is a) mon = 48 b) man…

A: The slope to any curve y is given by dydx at given point.

Q: B) Use Green's Theorem to evaluate F dr, where C is the triangle with vertices (0,0) (3,0) and (3,…

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Q: The intersection points between the curves r = 3. and r = are 1-cos e 1+cose

A: The given curves are, r=11-cosθ                      ........(1) r=31+cosθ…

Q: Find all angles between 0 and 2n satisfying the condition V2 COS T = Separate your answers with…

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Q: show that r = cos 2θ is symmetrical with respect to the horizontal axis.

A: show that r = cos 2θ is symmetrical with respect to the horizontal axis.

Q: az (b) Determine the by using the Chain rule with the following information: ds z = cos (x"y) – sin…

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Q: tan z, + tanz, = T-(tan z;) +(tan 72) tan(z, +2) ) Prove that: cos(z + w) = cosz cosw + sinz sin w

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Q: Transform F(s) (giving you cos 5t + t³

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Q: 1. Prove that the composite trapezoidal rule with h = 2-i, i E N, is exact for ſ cos? (Tx) dr

A: We know that in composite trapezoidal rule, we approximate the integral as follows: ∫abf(x) dx ≈  h…

Q: fhe coefpicient an fiderivative what? rin (2x ) in the fre of of F (A CoS is ン

A: We have to find the coefficient of sin 2x for given problem.

Q: Suppose z and y are funetions of time and satisfy the formula e sin y = In y + tan dy Write a…

A: Solution:- differentiate with respect to t.

Q: -W : By the same way, prove that g Z sinWo sinw.k Z -27 cus Wo +1

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Q: Show that the p.d.f. of Z? is given by g1(x) = cosh(vAr), x > 0, wh cosh(z) = }(e² + e-=) is known…

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: Evaluate . 2y2 cos(x) dx + 4ysin(x)dy where C is the line from (0,0) to G,0) and then a line from (,…

A: Line integral over the curve.

Q: Let S (-7, 7) x Rx {0} and S2 = Image() where (u, v, 0) = (cosh v cos u, cosh v sin u, v). %3D…

A: Given: S1 = ( -π, π) * R *{0} S2 = Image (ϕ ) In which, ϕ (u,v,0) = ( cosh v cos u, cosh v sin u, v)…

Q: The function f(x) satisfies the hypotheses of the Mean Value Theorem on %3D cos(z)+1 Select one: a.…

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Q: let Po)- tar'c) + tant (L). show that Plx)=C,where cis a constant and then Aind C

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Q: •2n Let a and b be distinct nonnegative integer. Prove that Sa sinax cos bx dx = 0 %3D

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Q: التاريخ اليوم موضوع الدرس A) Discuss the conrergence of facx) %3D on A = Co,0)

A: Convergence of the sequence

Q: Exercises 1) Find if z = 3 cos x – sin(xy),x = ,y = 3t -

A: The given equation is; z = 3 cosx - sin(xy) , x=1/t , y=3t

Q: Suppose that z is a function of z and y and that ze y cos z. Find and

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Q: Evaluate: / sech[in cosr Janx dx A -2 tan-1(e cosx) +c cOsx B) None 2 tan -(e cOx) + C COSA D - 2…

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Q: Find the projection of the function f(x) = cos2 x on the orthogonal set (1,cos x,cos 2x) on the…

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Q: Find the edlution of the following equstions: (osx<r) a) cosx- casx =0 . b) tan2x = 3 tan X Sin8X .…

A: We have to solve the following equations.

Q: 2t is the period of O f(t) = sin 2t %3D O f(t) = tan 2t %3D O f(t) = cos (1/2)t %3D O f(t) = cot…

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Q: 1. z, =1-j2 and Z,=2+j3; Evaluate cos[Z,J?

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: а. х %3 (3, —4,0, у b. х %3D (2, 1, —3, 4y c. x = (sen k, cos k, 24y para un entero positivo fijok

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Q: (a) Under the substitution, sketch a right-angled triangle and show that () 1 t sin 2 and cos 2 V1+…

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Q: (b) Show that U (x, y) = eu cos v, V(x, y) = eusin v are conjugate harmonic of each other if f = u +…

A: It is given that,  f = u+iv  is analytic. We have to show that,  U(x, y) = eu cos v  and  V(x, y) =…

Q: The Wronskian, W, of the functions y1 = sin(2x) and y2 cos(2x) is %3D

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Q: Is h: (-1,1) → R, h(x) = tan[(t/2)x] homeomorphism? Please search. 14:42 / %3D a

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Q: The integral S (A S- (в x dx x² + √√√x²-1- sino do 1 + cos sec²0 do 1+tano " cose de 1-sino sece…

A: Use trigonometric substitution

Q: do Evaluate the intergal using the residue theorem. 12 +1 cos 0

A: ∫02πdθ12+1 cosθLet, z=eiθ . Then cosθ=(z+z-1)/2, dz=iz dθ, so that∫02πdθ12+1…

Q: which u-sub will help integrate this? A. u = dx 11 [arctan(x)]" dæ = [9 + 12 cos(x)]" B. u 9+ 9x2 C.…

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Q: Consider J sin'x cos²x dx. If we let "=cos x , the integrand can be transformed to. A 2u2 - - | (u²-…

A: The given integral,     ∫sin5x cos2x dx

Q: (b) If u =x cosy+ ye», where x=s+2 and y= st, prove that 2- ds du - (s - 21) (* siny-xye -e").

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Q: Use the convolution theorem to show that cos T sin (t – T) dr 1 sin t. %3D 2

A: Convolution theorem use integration of product of 2 functions and transforms them to pointwise…

Q: Let f(x) = e cosx, sx %3D 2. Express your answers in exact form. ElN

A: Inflection point occurs when the second derivative of the function equals to zero.

Q: The Jacobian of the transformation ac=r cos 0, y =r sin 0 is r. Select one:

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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…

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Q: - Show that u(x,t) e-a't[A sin(2x) + B cos(Ax)] satisfies the PDE uz = a?uxx for arbitrary A, B and…

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Q: إعادة تعيين Q5. Let a and b be distinct nonnegative integer. Prove that sinax cos bx dx = 0 إلغاء

A: We will find the value of integration.  We know the formula of  2sinA cos B = sin(A+B) + sin(A-B).

Q: Prove the following hyperbolic trig identity. cosh(x + y) = cosh(x) cosh(y) + sinh(x) sinh(y).

A: cosh(x+y)=cosh(x)cosh(y)+sinh(x)sinh(y)

Q: Show that J, (z cos0)d0 = - R/2 os e)de = 1-cos z %3D 21

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Q: 5] Sketch the graph of r(t) direction of increasing t. (sin t, 2 cos t) and show the %3D

A: Given: r(t) = (sint, 2cost)

Q: Let fln) = e cosx, sx %3D Express your answers in exact form.

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Q: Compute the Jacobian of the mapping at the given point. O(r, 0) = (8r cos(0), 8r sin(0)), (r, 0) =…

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Q: Let = (sin x cos y, cos I sin y, In z).- Compute div i %3D

A: Given,          v→ =  sinxcosy , cosxsiny , lnz