Discuss passibility of existence f Selution u(x)-Sin10x t257 %3D K(z,t) = Sin(x+7) Sin[t-)3; 0xct %3D Sn(t+ /4) Sin(x-);textT Find the Selution exists.

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A: Consider the provided question, Analyzing the given function over the given interval using computer…

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A: This is a problem of Differential Calculus.

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A: Note :As per our guidelines we are supposed to answer only one question if there are multiple…

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A: Solved below

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A: We can evaluate the given integral by using the tabular integration by parts method.

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A: Evaluate the following 1-prove sin 2x+cos 2x+1/sin 2x-cos 2x+1=cot x 2-sinh(u-v) = sinh u.cosh v-…

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A: This question can be solved using the concept of integration of trigonometric function.

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A: Given integration is ∫sinlnxxcos2lnxdx We solve the integral using proper substitution.

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A: Let's find.

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A: i) Given that expression is sinx-3cosx.It is required to write the given expression in the form…

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A: To prove: ∫tankx dx=tank-1xk-1-∫tank-2x dx

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A: Given function,f(x) = sin(6x) , x0 = π12then, we have to find linear and quadratic approximation of…

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A: The graph of sin 3x is continuous on the entire number line.

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A: Given:     To determine: expression for du

Q: 9) f(x. v) = sin (x- 3y) Ans. f, =2sin(x-3y)cos(x-3y),. f, =-6sin(x - 3y)cos(x-3y)

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Q: Find the limits in Exercises 36-40  Are the functions continuous at the point being approached?

A: We’ll answer the first three questions since we answer only one question at a time. Please submit a…

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Q: 14) f' (x) =(sin 3 x)'=, A) – 3(cot2 x) csc2x C) 3(tan2 x) sec2x By Power Rule B) – 3 sin2 x cos x…

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Q: Integral proof Prove the formula f coth x dx = In |sinh x| + C of Theorem 7.6.

A: Consider the provided integral, ∫cothxdx=lnsinhx+C Show that the left hand side is equals to right…

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A: This is a problem of fundamentals of trigonometric identities. Please find the solution below.

Q: x3 + x2 ) lim x→-1 x+ 1| (i) ( 3 Vx2 +x +6+ Vx + 8 - 5x (ii) 6) lim x1+ x2 – x (iii) ( sin(3x)…

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

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Q: sin(5x) dx 2+сos(5x) اخترأحد الخيارات х + tan(5x) + с.ао —In | 2 + сos(5ӕ) | +с.Ь 1 +c.c 2+сos(5ӕ)…

A: Since , in the given integration problem we have derivative of denominator in numerator so we will…

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A: Since you have posted multiple questions we solve first question for you  To get the solution of…

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Q: IV. Integration by Part 1. | sin x sin 4xdx Scos cos 2x sin 3xdx 2. 3. (sin(In r)dr

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Q: (1-cos 6x)dx Perform the integration:S 1+cos 6x tanx - x +C c. tan3x – x+C A. -tanx – x+C D. tan3x –…

A: We have to choose correct option

Q: 3) Find the expention of sin³ 0 4) Proof that: cosh iz = cos z 5) Prove that: cosh² z - sinh²z = 1…

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A: Consider the provided question, The l2 norm or Forbenius norm(FN) is the square root of the sum of…

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A: Definite integration limit as sum

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Q: 2x² sin (x²)dx = V(1-x*) Select one: a. - sin-(x²) cos(sin(x²)) + x² + C b. - cot-(x?) sec(sin-(x²))…

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A: Topic = Integration

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.