Use the functions f and g in C[-1, 1] to find (f, 9), ||f||, ||9|l, and d(f, g) for the inner product (f, f(x) = 5x, g(x) = e¬* (a) (f, 9) (b) ||| (c) |l9|| (d) d(f, g)

Q: 2xy// + (x + 1)y/ +3y = 0

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Q: The domain of the function f(x) = v2x- 3 is -) a) b) c) (-0,2] d) (-0,3] b d. a O c

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Q: Q-5 Solve the boundary value problem (D? + 36)y = sin 6z given thaty(0) = 1 and y(0) = 2 Also check…

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Q: f(x) = -9 f'(x) = -(x²+9) (x²-9)2 f"(x) = 2x(x²+27) (x²–9)3 4. Given a) Provide a complete analysis…

A: a)

Q: a2f ду? 1 If f(x, y, z) = - 2+y² + find ax2 az2

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Q: The evaluation of S z dx is V4+x2 O In(sece + tan0) + c o - In(sec0 + tan0) + c c In|sece – tan0|+ c…

A: we have to evaluate the following integral .

Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: 1- Suppose A=

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Q: Use synthetic division to find 1"(-1) and f"(-1) where f(x)= 3x'-8x + 5x-2x' + 5x +13

A: To find the f'''-1 and f4-1 Given that the  fx=3x7-8x6+5x4-2x3+5x+13 f'x=21x6-48x5+20x3-6x2+5…

Q: And Justify True OR False f(a, b) = (a-2)² + (6-3)³. Then, we say Pornt (2.31 T f=R²-)R. is local…

A: Given                                                             The stationary point is

Q: a) f(x) = {(3, –4), (2, 1), (–9,–3)} |

A: We have to find domain and range

Q: Prove that F (3.x)(A → B) → (Vx)A → (3x)B. 3.

A: To prove: ⊢∃xA→B→∀xA→∃xB

Q: Z is the set of integers, R is the set of real numbers. 4) Find the inverse of functions a) f:…

A: (a) Consider the function, f:[0,∞)→[0,∞) defined by fx=x2+12 For x∈[0,∞), fx∈12,∞. That is, range…

Q: Exercise 5: If f(x) = x5 + 2x³ + 2x, check that f is injective and find (f-1)'(-5).

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Q: Which one of the following is isomorphic to Z4 x Z6/((2,4))?

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Q: Find the polynomial f(x) for which x· f(x – 1) = (x – 3) · f(x), Væ |

A: find the polynomial f(x) for which  x fx-1=x-3 fx ∀x for x=0 x fx-1=x-3 fx ∀x

Q: Prove that In( +VI-X²³) = In ( ¹+ √1-x²) sech ¹(x) =

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Q: Suppose f(x) = Evaluate: f(x) dx (A - In (2) (B) 4 3 16 (D) In (2)

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Q: Find a polynomial f with the following properties: i) f is concave up on (-, –2) U (0, ∞) and…

A: Function and derivative

Q: Let f(x) = Vx and g(x) = x³ +1. Find 29 a) f(g(2)) b) g(f(4)) c) f(F(16)) d) g(g(0)) e) f(2+ h) f)…

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Q: 2 - Find: (a) 3a ,(b) a +b , (c) a-b , (d) la + b|, (e) a- b|, (f) 3a – 4b and (g) | 5a + 2b|. If 1.…

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Q: Write the composite function in the form Køtx)). [Identify the inner function u - g(x) and the outer…

A: We need to find out functions y=fu and u=gx We need to make a composition of the functions f and g…

Q: That  f(x) = -2x,    g(x)= |x + 4|, and h(x)2/x-3. Evalute the functions for the given values of x:…

A: a) Obtain (g o f ) as follows.