Differentiate the function: y = e-x cos²x x²+x+1

Q: Find the derivative of the following functions. Use long method. a. f(x) = 3x² + 5x - 100 b. f(x) =…

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Q: As you are walking in the forest you look up just as a boulder becomes dislodged from the side of a…

A: topic- algebra

Q: Find f. f(t) = f"(t) = 5et + 6 sin t, f(0) = 0, f(T) = 0

A: On solving this we will get

Q: 3 [² [v³ – y³]³ª a Jo ² dy

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Q: II. Consider the circle C1 : r = 1 and the roses C2 : r = cos 2θ and C3 : r = 2 cos 2θ, each of…

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Q: 3- Air at 25°C and 100 kPa at a relative humidity of 75 percent. The parti pressure of water vapour…

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Q: Example 3 Find the centroid of the region bounded by y = x³, x = 2 and the x-axis.

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Q: S N

A: Use ratio test for checking the radius of convergence

Q: FIND THE AREA BOUNDED BY THE PARABOLA x = 8+2y-y², THE Y-AXIS, AND THE LINES y = -) AND y = 3

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Q: Solve f(x + 1)(x + 2)²(x² − 1)dx with and without the even-odd theorems (show both solutions).

A: Solved below.

Q: Suppose that A, B, C, D, and E are matrices with the following sizes: A B C D E (4 × 1) (4x4) (4x 1)…

A: We know that matrix multiplication AB is defined only if number of column of matrix A is equal to…

Q: 4. Verify the final value theorem for the function 3t²e-4t and determine its steady state value.

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Q: (a) Find the exact area under the curve y = 1/x³ from x = 1 to x = t for t = 10, 100, and 1000. t =…

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Q: State the initial value theorem. Verify the theorem for the functions: (a) 3-4 sin t (b) (t-4)² and…

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Q: Find a particular solution of as =10csc² 2t determined by s= 2 when t == . dt

A: dsdt=10csc2(2t)  s(π/4)=2 ds=10csc2(2t)  take integration both side

Q: -x+1 3+z Given the points R (1, -1, -3), the vector v = and the line d: = 1 + y = 3 2 1. Determine…

A: Both questions are solved.

Q: Find the derivative of f (y) = 8 tan (y) V √y 8 8 √Y y4

A: The given function is: fy=8tany-y8-8y4y As we know that; The Sum/Difference rule: f±g'=f'±g' The…

Q: Suppose that f(x) = x² − 3x + 2. Then there is no critical number to determine concavity. Select…

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Q: S² z²√√(-z² + 1)5 dz

A: To find the value of the given integral.

Q: ds Find the complete solution of = 8t³ √√s. dt

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Q: R(t) = (2 In|sec tl, sin 2t, cos 2t) Find the distance travelled by a particle along the curve…

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Q: A rectangular field having an area of 2500m² is to be enclosed by a fence, and two additional fence…

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Q: x² 1) Let f(x) (Figure 24). Verify the X 1 following: (a) f(0) is a local max and f(2) a local min.…

A: Since you have posted a question having multiple subpart part as per guidelines we can solve only…

Q: √√7 - t³, cos t³) t³, c 3 R(t) = (sin t³,-

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Q: Solve f(x + 1)(x + 2)²(x² - 1)dx with and without the even-odd theorems (show both solutions).

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Q: Find the Area of the Surface obtained by rotating the curve about the y -axis y = √√x, 1 ≤ y ≤2

A: Given y=x13    1≤y≤2Rotating about y-axisarea of surface of revolution about tghe y…

Q: 9. y(y² + 1)dx + x(y²-1)dy = 0 Ans: + xy = c

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Q: Consider the vector-valued function R(t) 1. Find the domain of R. 2. Show that R is continuous at t…

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Q: Let C be a curve with the parametric equations à = − ln(t + 1); y = sint, t = [0, 1]. a. Set-up the…

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Q: Find a particular solution of =(x−1)² if y=-21 when x=-3. dx

A: dydx  = ( x - 1 )2   , y = -21, x = -3 we have to find particular solution of it

Q: 2 2 2 Find the moment of inertia: x3 + y3 = a3 about x = = 0.

A: Let's find moment of intertia.

Q: One of the correct steps to evaluate A sin²20d0 [² B cos 40d0 C) None Ⓒ//ww D do + sin²20d0 Ⓒ = [ √…

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Q: Consider the point P (-3,-1,5), the line : x = 3 t. y, y = -6t -3₁ z = 2t +1, and the Flane 1² : 7…

A: Given

Q: i can't understand your solution

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Q: S√4t² + 3 dt

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Q: If C = {(x, y): 1 ≤ x ≤ 2, y = ln(x + √x² − 1)}, find the length of the curve. -

A: C=x,y: 1≤x≤2, y=lnx+x2-1

Q: x-4 x²+2x-15 Inx+51-Inx-31+ C 8 Option 1 S: dx 1 (x + 5)⁹1 Je In + C + x-3 -100 1 9 In|x + 5|ln|x −…

A: We can find the answer as below

Q: √√f(x) x→ 3.h(x) 20. What is the value of lim A. C. - 12/2 6 B. -1 D. 21/2 5 I N|2 13 -?

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Q: Find the area bounded by the parabolas (x - 2)² - 9py = 0 and y² = 9p(x-2).

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Q: Evaluate the y' and Simplify the answers I Direct trigo functions y = x² sinx + 2xcosx - 2sinx

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Q: If a sphere passes through the points A(0, 1, 2) and B(−1, 2, 2) and its center C lies on the…

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Q: The gradient of the tangent to the curve y=-3x³ + 4ax² - 5x + 4 at x = 1 is 2. The value of a is 2.…

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Q: Determine the Cartesian equation of the tangent line to C1 at the point where 0 = π/2. Given: polar…

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Q: Evaluate the following integrals. 13 1 sin²x -dx

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Q: d The series is divergent. . Ignore "Give your reasons" below. There is no need to give reason.…

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Q: Find the average value of f(x, y) = sin(x + y) over a. The rectangle 0≤x≤ 1,0 ≤ y ≤ n b. The…

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Q: Let line 1: x = = = and point P(1,0,1). 2 ● Find the set of parametric equations of the line…

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Q: Let line l : x=y/2=z/3 and point P(1,0,1). Find an equation of the plane (in point-normal form)…

A: Solution of given question is written in below steps.

Q: Find the volume of R using shell method, when R is bounded by y = 4x - x², y = 0 about the line x =…

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Q: What integration technique can be used to integrate: O Integration Formulas O Trigonometric…

A: Use integration by parts and substitution method.