EX:- Find the inverse F.T. of F(W) = |n|2+jw/. J Sols du F(W) 2 + jw *j jd FCW) = = dw 2+jw ƒ [j+=+=+Fcw)} = f[ = = = } ⇒ t f(t) = = f(t) 2t 2 a+jw + >0 -2t e

Q: Calculate M6 for f(x) = v2x over [2, 5].

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Q: 1. O A. 4 +0+ ヤ+LXA 3 x² 1 O B. (x? + 4) /2 - 4x² + 4 +0 312

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Q: 1. Find the following for the function f(x, y) = 3x³y² - 5x + 26y - 9.

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Q: /s. 5. Show that 2x?dx = f 2x²dx + S, 2x²dx + f 2x²dx %3D

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Q: Calculate R3 and L3 for f(x) = x2-8x+2 over [1,4] .

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Q: Write f(t) = 7e.8t in the form f(t) = Pob' and determine Po and b. (Give exact answers using…

A: given that  f(t) =7e1.8t  = 7(e1.8) t .......... (1)  and f(t) = Pobt............ (2)  Now on…

Q: Calculate R3 and L3 for f(x)=x2−4x+5 over [1,4].

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Q: Evaluate f (tcos² ti+1/tj+sec² tk) dt

A: To solve the following

Q: Consider the point (x,y) lying on the graph of the line 8x + 7y = 3. Let L be the distance from the…

A: We use the distance formula

Q: If y =f (x) is a function in x then prove that f(a + nh) ="C,f(a) +"C, Aƒ(a) +"C,ƒ(@) + +"C, A"…

A: Given: y=fx is a function in x Prove that: f(a+nh)=C0nfa+C1n∆fa+C2n∆2fa+…+Cnn∆nfa…

Q: Evaluate F.dr where F(x, v)=xyi (4, 0).

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Q: Find Vf(a), given the following data. 91 Calculate 91, 92 and 93 such that Vf(a) = 92 93. 91 92 93 =…

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Q: Find all local extrema of the function f given by f : R? → R, f(x1, r2) = 3x7x2+ x} – 3a? – 3x3 + 2.

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Q: Find fx and fy for f(x, y) = (1 - 2x + y)ex+2y Select one: a. None of these b. fx = c. fx (2 + x -…

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Q: Let f(x.y) = In ( x2 + y ). If f,(2,a)=f,(- 1, 2), what is the value of a? O a. 6 O b.3 O. 7 O d. 8…

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Q: Let f(x, y) = 3x² + 4y? – axy. (a) Find the values of a such that the graph of f increases when…

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Q: Calculate R3 and L3

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Q: Use the IVT to show that f (x) = x3 + x takes on the value 9 for some x in [1, 2].

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Q: Differentiate the following function. 6x2 +5 y= x2 +1

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Q: find the derivative of (2³ + j)² O 23 +j O 223 + j O 625 + j6z² O 325 + j3z?

A: Derivative of (z3+j)2 is 2(z3+j)2-1(3z2+0) = 2(z3+j)×3z2 = 6z2(z3+j) = 6z5+j6z2

Q: .7 Evaluate ſ x³tan-1x dx.

A: The integral is given , ∫x3tan-1x dx. Solve the integral by integration by parts, ∫x3tan-1x…

Q: Find real numbers a,b,c,d such that And then find f'(z) =? f(x) = x² + axy + by² +1(cz² + day + y²).

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Q: Differentiate the following functions using product rule. 1. f (æ) = (3x – 9) (x – 6) 2. ƒ (x) = (æ³…

A: The product rule of differentiation is given by: ddxf.g=dfdx.g+f.dgdx

Q: h. By completing the square, re-express fx,y (x, y) in the form fx,y(x, y) = e-(ax-by)² e-cy², Where…

A: Suppose X and Y are jointly distributed with pdf  where .

Q: Express the function in the form f°g 1. 3 G(x) 3 2 а. f)x, g) -2 b fx)x, g) 2 с. g(x) x fx) 2 d…

A: “Since you have asked multiple questions with multiple sub-parts, we will solve the first three…