8) A functrin fux) io de finied as fohons, ex'-18 for * +3 x - 3 for x= 3 Find the value of k so thent flx) is continuons at x = 3

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Q: 28- For What values of a anel ら -2 fCx) = ー<くく %3D ax-b Continuons at every x ?

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Q: 3) Prove that c) cosh2x = 1 + 2 sinh? x

A: In the question we have to prove the given function.

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A:

Q: 29 - For what values of a and b is | S x+3a-b axt 26 3x-5 Continuows at every X?

A: g(x)=ax+2bx≤0x2+3a-b0&lt;x≤23x-5x&gt;2

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Q: Find the of Integ ration f(u)= tanu + Cos 2u. %3D

A: Given information is :

Q: Suppose tan u = %¾ (sm u>0) and tanuo12/5 Ccasx cO]. Ead he exsee velos OR the followly trgeronetnc…

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Q: satisfies thé équation:y + 13y - Show that y=e Sin 3x

A: Topic = Derivative

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Q: Let C be the shortest path that connects a to zi and I = f. (sinhz + 1)dz. Then None of these…

A: Second option is correct answer i. e.  I= -1-cosh(π)+π(i-1) . Thankyou !

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Q: 8F OF OF 1. Use the formulas above to find and ду ax exy + sin (xyz) + In (yz) = 4 – z

A: Partially differentiate the function with respect to x.…

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A: Given: 53.   fx=xlnx,  0,∞

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Q: 1 dy sin¬' x If y = xv1 – x² + sin=1 x, prove that 24 – 2

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Q: „In sec²(sin2y)dy can be evaluated by writing it as sec2y A sec²(sin2y) - cos2ydy None © In…

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Q: 1. If Y= 4 In (In (In(sec(x)) then Ý=[4 (tan)/{ In ((In (sec)) In (sex)}]

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Q: Use the trapezoidal rule withn= 4 to approximate %3D cos(x) COS

A: Given: n=4 and ∫15cos(x)xdxwe know that trapezoidal rule for approximating ∫abf(x)dxis given…

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A: Cauchy's integral formula : Let U be an open subset of the complex plane C, and suppose the closed…

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Q: 5. Verify whether the function f(z) Cauchy-Riemann equations or not. sinh 4x cos 4y + i cosh 4x sin…

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Q: Let C be the shortest path that connects t to ni and I = S. (coshz + 1)dz. Then I=0 1--sinh π+…

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Q: 4. A force of F(x) = x - cos(3x) + 2,x is in meters, acts on an object. Identify the work required…

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Q: (§5.4, Q42) Calculate So™ f(x) dx, where sin x, x T

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A: Given:

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A: The equation of hyperbola is xa2-yb2=1   The right branch (x&gt;0) of the hyperbola can be…

Q: then what is y at x=1?

A: We can find y at x=1 in the following steps.

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Q: plot Y funetion of as over Hhe Peenge ☺.0l <*< l00.

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A: The volume of the solid formed by revolving the region bounded by the curve y=f(x) and the x−axis…

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Q: Hico/ prove Thall Cosh2: - 2 tañ z Sinhz: 1+2 Tanhiz =

A: Since you have asked for a question with multiple sub-parts , we will solve the first three…

Q: 2. A. If : = sin(3x+2y) , verify that 2 -3 = -6z ax2 B. If f = x³y3 + 2xcosy + y?lnx then show that…

A: x=sin (3x+2y)

Q: я/4 4 sin (4t) dt. 9- cos (4t) Evaluate the integral я/4 4 sin (4t) dt%3D 9- cos (4t)

A: Use integration by parts

Q: 8. 4 6° sin°3ycos *3y dy

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Q: The singularity at 0 of tan is isolated. Select one: O True False

A: If p€S-S' iff p is isolated singularity.  Where S=set of singularity.  And S'=derived set of…

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Q: If y=tanx , prove that y```=2(y^2+1)(3y^2+1)

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Q: tost con Vergen ce and divergence 2 Lnn /-

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Q: 4 Find the mul hiplicity of the foll owing faunchons 3 2. a-9xt 30 L -4yx at x= 3 and x=2 3. 2. ) f-…

A: We will first check whether the given values are roots of function, then we will find the…

Q: 1 Use the definition of the hyperbolic functions to prove the identity 1- - tanh? (2x) cosh (2x)

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Q: derrivative of: Cos(xy)+secy=5

A: Consider the given expression as cosxy+secy=5

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Q: 1. y = Arctan 3-V9-x2 2. y = 4 Arccos + 2v4 - x2 2 y = In (*+2), (x-1)2 3. у%3DIn

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Q: Prove that for all x € [1, 00), – sinh (- |cosh'(x)|) = V -1. %3D Ouest!

A: Proving of function  sinh(cos-1(x))

Q: If when infinitely differentiable function Cv.y)= (13.4). X=r COSX ノ 3, 1) at point 2a=-2, zrr=0,…

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Q: 5.If the tangent 1ine to the functlen fx)= axt-6x at X=- has the equatfon. y= 3x+2then 6=?

A: