6. Let u (x, t) be the solution of the initial-boundary value problem U = 0 < x < 4, t> 0, Uz (0, t) = ux (4, t) = 0 t>0, u (x, 0) = 2 – cos (Tx) – 7 cos (5tx) 0 < x < 4. What is lim u (x, t)? A) 2 B) 0 C) -00 D) E) The solution oscillates and does not reach a limit 8

Q: 10. Given: f(x) 3= d) tan(A – B) and g(x)=x² +8 x- 5 Find: a) (f-g)(x) (g •(8))(x) i) (g-f)(3) b)…

A: Given that f(x)=1x-5 and g(x)=x2+8   (a) f-gx f-gx=fx-gx               =1x-5-x2+8…

Q: TLP iadade mnts & smt Findf F'(t) =sec(t) (seclE)+ tan (ED), -st < f- FCt) = -<ts f (--7 2.

A: We simplify f'(t) by expanding  To find f(t) we integrate f'(t) C=integrating constant

Q: What is the linear approximation of this function at (1,0) F(x, y) = (F(x, y) = (x² cos(x+y)) x²y 0…

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Q: (а) 1716 — 8г' + 3х — 4 + 1/3 + Vт — V:3 (b) sin 5a - сos(х /8) + sec?(z/3) csc (5x) сot (5x) (с) 2…

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Q: 3. Let h(x, y) x + y sin²x 2¹+ y² 0, if (x, y) = (0,0) if (x, y) = (0,0) (a) Show that h is…

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Q: For what value of the constant cis the function f continuous on(-0,0) x2+ 2x +6 if xsZ cosin (x-2)…

A:

Q: If f(x,y)=log, (cos²(e* ) +si f(x,y) is ây ôx + sin(x+ y) then %3D

A: Given that: fx,y=logecos2ex2+sinx+y To determine ∂∂y∂∂xfx,y

Q: 13. Find ƒ. (1)ƒ'(x)=x² + 3√x (2) f(t)=2cost+sec²t,-/2 <t</2,ƒ(π/3)=4; (3)ƒ*(x) = 6x+sinx.

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Q: E Let C₁ be the curve parameterized by r(t) = (cos² t, sint) where t = [-]. Let C₂ be the line…

A: Given that C1 is the curve parameterized by r(t)=(cos2⁡t,sin⁡t),t∈[−π2,π2].Let C2 be the line…

Q: 23. Integrate: S x+2 dx 2 A. V1– x² + Sin-1x + C C. -V1– x² +Sin-1x + C B.V1 – x2 +Sin-1x + C D. –V1…

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Q: 4. Determine all possible functions f(x) that satisfy the given conditions. (a) f'(x) = V¤ – 3 x2…

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Q: (a) Define the symbols ôf/DE and af/dz by af 1 (af 10f 2 (dr af 1 (of 18f i by, dz 2 dr' i dy as…

A: Since you have asked multiple questions, we will solve the Question (a) for you. If you want any…

Q: 1.30 These prove that isomorphism is an equivalence relation. (a) Show that the identity map id: V →…

A:

Q: 1. Let V (x, y) 1+ x2 + y 1+x² + y* and let F(t) = x(t)î + y(t)ĵ where cos(t) (cos (t) + cos²(t)(2…

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Q: Let 7(t) = Find '(t) F (t) =

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Q: F = X 1 + y (tany) j x² + y² = 1 →X Greens theorem

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Q: e) S (x² – 2 x + 1)dx

A: According to Bartleby's policy we are allowed to solve only 1 question at a time. Here's the…

Q: i) Given that f(x)=3cos5x+sin5x. (a) Express f(x) in the form Rcos(5x-a) where R>0 and 0° < a <90°.…

A:

Q: In (21y) = 7x + 21y is an equation that defines y as an implicit function of x, one of th…

A:

Q: Q3/ If f(x)= x=2x+1 X71, a=2 Find the followings; a) f(x) = x b) show that f(f(x)) = f (f(x)) c)…

A: "Since you have asked multiple questions with multisubparts, we will solve the first question with…

Q: The interval on which the graph of f (x)= cos 2x, xE 0,7 is concave up is: %3D 37 (A) t 37 4 4 (B)…

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Q: 5. Find L{f(t)} a. f(t) = sin?(t) + t b. f(t) = n² – 8e¬2t + (et + 1)² | c. f(t) = F, sin yt -cos…

A: As per our limit we can solve only first three subdivisions if you want the answer for other…

Q: 1. ('88 BC) The length of the curve y = x³ from x = 0 to x=2 is given by 2 2 A) [√₁ + x ²dx (B) √ √…

A: Given,.Formula for length of the curve is,

Q: b) y = cos(5x) ln(x² + 1).

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Q: The graph of f(x)= x2 -1 is concave up on interval (-1,1)^O (0,1) 0 (-1,0) U (1, 0 )co…

A: Given,  The function fx = xx2-1  We have to find the interval in which the graph of  fx = xx2-1 is…

Q: The conjugate harmonic function v(x, y) of u(x, y) = In (x2 + y2) is *() + 1. 2tan -1 2tan-1 + C ()…

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Q: 4. Use Laplace transforms to solve the following initial value problems. (a) y"+2y-3y = 10 sinh 2t,…

A: Laplace transform.

Q: A. Find the solution of the following differential equations. b4y=5x

A: This is a question of DE.

Q: 3) Determine the domain and range of the following functions i) f (x,y) =x^2 + y^2 + 2  ii) f…

A: As per Bartleby guidelines for more than three subparts in a question only first three should be…