Take xlt) then x (10) = X => x/w) = Ś j'₁. é just dt = x(w) == 1 ζω X/W) = Lx -jwt -jw jw -jw 1 - -jw 2j ju X2 Seax d = eax a How did the signal change from negative to positive?

Q: Find the gradient of the function at the given point g(x, y) = 2xe/x, (16, 0) Vg(16, 0) =

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Q: Sketch the region that corresponds to the given inequalities.   12x  +  6y ≤ 60   6x  +  12y ≤ 60…

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Q: ar lim ƒ(x)=-1 2) 1 →→2 Given find the following lirnit 3/7f(x)- g(x)² g(x)+1 lim 2 and lim g(x)=1…

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Q: (a) Use differentiation to find a power series representation for f(x): = f(x): 8 = Σ(1 n = 0 f(x)…

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Q: 1. Show that (a) exp(2±3лi) = -e²; (c) exp(z+лi) = - expz. πί p ( ² + 7² ) = √ = (1 + i); 4 (b) exp

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Q: Determine whether the series converges or diverges. 00 3″ 3 + 50 n = 1 The series converges by the…

A: Solve the following

Q: Suppose f is a differentiable function with f(1) = 1 and f'() = -1. Let y = f(x). tanx + ex. cosx.…

A: According to question,Given Function,y = fx.tan x + ex.cos xfπ = 1andf'π =- 1

Q: y' =+y(y+2), y(0) = - 1

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Q: Verify the identity. 9 cos(sin ¹ x) = √81 - 81x² = 8 = x = . Thus, Let 8 = sin-¹ x = sin 8 = x 9…

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Q: Find the area of the region. 2 16 x y =

A: To find thae area of the given region

Q: Express lim Σ n → ∞i=1 3 n ( n 3i + COS 9/² 2 as a definite integral

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Q: 11 7 Find Y y N 2x² + y² = 4 2

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Q: Find the lengths of the sides of the triangle with the indicated vertices, and determine whether the…

A: A detailed solution is given below.

Q: n√In(4n) n=7 O convergent divergent

A: Divergent. Test used is integral test.  If integral of the terms of the series is convergent then…

Q: Find the angle between the vectors in radians and in degrees. u = 8i + 3j + k v = 3i - 8j (a)…

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Q: Find the component form of u + v given the lengths of u andy and the angles that u and v make with…

A: We can solve this as follows:

Q: f(x) = 1 |x - 51 (a) Find the critical numbers of f. (Enter your answers as a comma-separated list.)…

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Q: A definite integral property says f₁² ƒ' (x) dx + f² ƒ' (x) dx = S² ƒ' (x) dx. What is ff'(x) dx? O…

A: Given graph of f'(x)

Q: O Defennire it the following series is Convergent оп divergent E n=1 3 मकर Determine if the…

A: Solve the following

Q: 3. Find V x F for F(x, y, z) = -xZ x² + y² i+ -yz x² + y² =j+ x² + y²k.

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Q: 3. Find V x F for F(x, y, z)= -x2 i + x² + y² -yz x² + y² =j+√x² + y²k.

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Q: Consider the following functions. f(x) = 6 sin x g(x) = 6 cos 2x Esxst Sketch the region bounded by…

A: Given f(x)= 6 sin x g(x) = 6 cos(2x)  in the interval -π2≤x≤π6

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A: Given :fx,y=sin8x+yp0, π

Q: Find the solution of the given initial value problem:

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Q: Given H(jw) -(4+jw) 6+5jw-w² an rewrite as:- (jw+4) -+₁) 6+ (jw)² + 5jw (jw+ 4) (jw+3) (jw+2) (jw+3)…

A: Topic:- application of calculus

Q: The area of the sector of a circle with radius 16 feet formed by a central angle of 95 is feet.…

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Q: 5 Plot the point P that has Cantesian Coondinates (x,y) = (4√3,-4) and then polar coordinates (1₁0)…

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Q: Find the general solution of the differential equation y" y 42y = -122t+84t². - - NOTE: Use t as the…

A: Follow the procedure given below.

Q: Evaluate the integra dx √2x-x¹

A: ∫12x-x2dx

Q: Consider the following. u = -9i2j4k, v = 2j + 2k (a) Find the projection of u onto v. (b) Find the…

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Q: Consider the following equations. f(x) = x5 + 3 g(x) = x + 3

A: Given equations f(x)=x5+3g(x)=x+3First we need to find the intersection points…

Q: Suppose that f(x) = /'(-2)- - f'(1) = 6x + 16 X Evaluate each of the following:

A: we have to find derivative at a point

Q: The derivative of a function at each point is itself. y=kex

A: To find out the derivative of the function.

Q: Find the derivative of f(x) = log, (3x4 − 2x²) at the point x = 3. Enter an exact answer. Provide…

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Q: Find dy/dx for 2x+y³ = 2y A B D bevelled fraction numerator d y over denominator d x end fraction…

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Q: Suppose the centripetal acceleration of a particle moving in a circle is a = where v is the velocity…

A: Please see the below picture for detailed solution.

Q: tan x 3 sec x If f(x) ƒ'(x) = To two decimal places, ƒ' (1) = =

A:

Q: 1. Given r(t) = <In(cost), -1, 2 $₁ 2 A a) Find the length of the curve for r(t) at 0<t< R|4 b) Find…

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Q: Find a basis for and the dimension of the solution space of the homogeneous system of linear…

A: The given homogeneous system,x+4y-2z=0-3x-12y+6z=0

Q: A parametrization of curve describes the specific time and location of a particle moving along the…

A: To sketch the curves xt=t2-4, yt=t2 for -2≤t≤3 and xt=4t2-4, yt=t for -1≤t≤32 and evaluate their…

Q: dx 2+2 sin x + cos x

A:

Q: A function is given. g(x) = 7 +  1 2x;    x = 1, x = 7   (a) Determine the net change between the…

A: Given the function gx=7+12x , x=1, x=7

Q: A solution to the DE ydx-xdy=0 is A B C D xy=C x = Cy none of these x=y=C

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Q: 2 = (x10 (ن) . A (b-a) [(ejob ejun -e سلم) ] - Coll - وسلام

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Q: 1o₂ = 2 · (² x (t) ·cos (nwot) at + = + [² 2 a 2¹ (1-4) Cos (2nit) dt =21 (1-t) 2 [- (t-1) Sin…

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Q: For the next two exercises, determine whether the integral converges or diverges. f 4 dt sint + √t 5…

A: For (5),…

Q: Given y(4) - 6y" - 36y" +216y' = t² +8+ t sint, determine a suitable form for Y(t) if the method of…

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Q: 3 dx 00 (2²+4)³/2 es or diverges.

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Q: Write and find the general solution of the differential equation that models the verbal statement.…

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Q: The particular solution of (2x+3)y'=y+ (2x+3) ¹/2 ; y ( − 1) = 0 using LDE is A B C D -2y=√√2x +3 In…

A: Please see the below picture for detailed solution.