Using the inner product (, ) : C( [0, 1] ) × C'( [0, 1] ) → R, (f, g) = √ 5 3 2 2 • ( ²2 ( - - ² ), ² ( x − 3 ) ) · X X 4 11 calculate

Q: Q2) a) Find Maclaurin expression of f (x) = Cosh (x) b)Find the gradient of the function f(x, y, z)…

A: Part (a) General form of function fx is Maclaurin series is…

Q: f= x? + क) | + ला (i) of =? (üi, af मु] liv) of

A:

Q: Calculate r' (t) and T(t), where r(t) = (2t - 7,2 – 5t, 3 + 5t). r' (t) = (2 T(t) = -5 5

A:

Q: Calculate r' (t) and T(t), where r(t) = (6 +5t,9 – 61, 2t). r' (t) = ( ). T(t) = ( ).

A:

Q: Find f'(2), where f(t) f'(2) = = u(t) · v(t), u(2) = (2, 1, −2), u'(2) = (7, 1, 8), and v(t) = (t,…

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Q: find (a) r'(1), (b) r"(1), and (c) r'(f) • r"(f).

A: The derivative of a position vector gives the rate of change of position of the body or the velocity…

Q: f(X1,X2) = f(X1). f(X,) If are not 1 independent then ylgn

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: The domain of F(x, y) =x*y+ x*+ = 1 D =R²- {(0, -)} A O D=R BO D=R? .C O D=R-{}

A:

Q: Find f '(2), where f (t) = ü(t) · i(t), ü(2) = (1,2,–1), ū'(2) = (3,0,4), and v(t) = (t, t?,t3).

A: To find out the f'(2)

Q: f(X1,X2)= f(X,).f (X2) If X,~N(H1,0) X2~N (H2,0) are not independent then ylgn ihi

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find r'(t), r''(t), r'(t) · r''(t)

A: According to bartleby guidelines we supposed to do the first three subparts of multiple subparts…

Q: Utilice la regla del producto para derivar y = (2x² + 2x + 1) (3x - 4) Llene los blancos (sombreados…

A:

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: Suppose X,~ Uniform(0, 2) and X, ~ Uniform(0, X,). Find E[2X,+X,].

A: Given,X1 ~U(0,2)X2 ~U(0,X1)E(X1)=2+02=1E(X2)=X1+02=X12

Q: let it be 2= f(x,y) and Y=tan' () and X = === In (r²+5²) Prove that fxx+fxy= (y² + S) (fr+fso)

A: We have to prove

Q: Display the discontinuity of h at (0,0) and Evaluate hx(0,0).

A:

Q: Find r'(t), r"(t), r(t) r"(t), and r(t) x r"(t). r(t) = 32²1 - 4tj + 12³k (a) r(t) (b) r"(t) (c)…

A:

Q: 1) FIND F'): C P)= (x D(2x+)

A:

Q: Let f(u) = u* and g(x) =u = 2x* + 6. Find (fo g)'(- 1). (fo g)'(-1)= (Туре an exact answer.)

A: Given:- Let f(u) = u4 and g(x) = u = 2x4 + 6   To Find (fog)'(-1).

Q: Let f(2) := 25. Show that f is invertible in a neighbourhood of i and calculate (f-1Y(/(i)).

A: Let f(z) = z5, show that f is invertible in a neighbourhood of i and calculate(f-1)' f(i)

Q: f" > 0 on (-∞, -1) U (-1,0).

A:

Q: Find r'(t), r"(t), r'(t) •r"(t), and r'(t) x r'"(t). r(t) %=D 흑래- 26j + 하하k (a) r'(t) (b) r"(t) (c)…

A:

Q: 3 prove that sinh (2) isine

A: Since you have posted multiple questions, we will provide the  solution   only to the first question…

Q: Show that fi (x) = cos x , f2(x) = cos 2x are orthogonal on [-7,71]. %3D

A: This is a application of integration problem

Q: Let r (t) = The dot product r (1) · r ' (1) =

A: First differentiate at given value then take dot product

Q: Find r'(t), r"(t), r'(t) ・r"(t), and r'(t) × r"(t). r(t) = 클레 - 3tj + (a) r'(t) (b) r"(t) (c)…

A: We need to find derivative and dot and cross products.

Q: Letr' (t) = (3 + 4t, cos(t), 6e³t) and 7(0) = (7, 2, 5). Determine r* (t). r(t) = ([ (..)

A:

Q: f : R --> R is defined by f(x) = 2x+1, A= (0,1)  and B = [ -1,1 ]    find f [A] and f-1[B]

A: