Q: 1. Given the space curve r(t) = (2e¹,e²¹.e^¹), find the curvature at t = 0
A: I am attaching image so that you understand each and every step.
Q: 2. Find the equation of the line tangent to the circle x + y + 6x - 2y - 15 = 0 at the point (1,-2).
A: x2 + y2 + 6x -2y -15 = 0 given we have to find equation of tangent line to circle for that first…
Q: A solid of revolution is formed by revolving about the x- axis the region bounded by the curve y √2x…
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Q: Use the comparison theorem to compare Enter your answer using either ≤ or >. F = = [₁* (√x + I + 2)…
A: We will use comparison theorem to compare the given two Integrals.
Q: 4 (A): If A 2 2 1 Find AB and AC. 01 0; 1-2 -1 1. 2 B = 2 ܚ ܨܢ ܝ 1 ܚܕ ܨܐ ܝܕ -2 -2 and -1 2 1 C: 11…
A: Here, the given matrices are: A=420210-2-11, B=2312-2-2-121, C=31-3026-121
Q: Compute u v if u and v are unit vectors and the angle between them is R|4
A: we know that u.v =uvcosθfor unit vector u=v=1given θ=π4
Q: x+2 3.) (x²-1)(x²+1)² of factor. dx; Solve by using partial fraction. Indicate the type
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Q: Q1/ Solve the following differential Equations. 1- (1+x2)dy-xy dx = 0
A: To solve the differential equation.
Q: Find the mass and the center of mass of the lamina with density 8(x, y) = √y x² +1 the rectangular…
A: We have the following formulas(i) Mass of a region m=∬δ(x,y)dA, where δ(x,y) is the density and dA…
Q: Find the general solution of the differential equation y" 10y' +61y = 0. NOTE: Use c₁ and ca as…
A: find the general solution of differential equation y"-10y'+61y=0
Q: Find the general solution of the differential equation y" 10y' +61y = 0. NOTE: Use c₁ and ce as…
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Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol: 1-cos x - sin²x
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Q: The answer above is NOT correct. Find the area of the region enclosed between y = 4 sin(x) and y = 3…
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Q: (A): Solve the following linear equations by Cramer's rule: x + y + 2z=1 2x-y-z = 0 = 4 x +2y-z
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Q: Given f(x) = 3x³ +22x² - Part: 0 / 2 Part 1 of 2 -21x-40, answer the following. Factor f(x), given…
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Q: Find the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM. A $124,000 trust is to…
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Q: Consider the following function. f(x) = x¹/3 + 4 (a) Find the critical numbers of f. (Enter your…
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Q: Given F(x) below, find F'(x). Provide your answer below: F(x) = I 4 (414 + sin* (t)) dt
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Q: Use the divergence of the vector field to compute F(x, y) = (tan-1 (2²)) i + (xy-2 +82²) j 4 fo…
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Q: In Problems 17-26, solve the initial value problem. dy y(0) = √3 dx y' = x³ (1-y), 1 dy 2 dx dy…
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Q: Using the Factor Theorem, which of the following is a factor of the polynomial function f(x) = 5x² +…
A: Given polynomial function is f(x)=5x3+5x2-60x
Q: what is under the 15872 is that a 9
A: The given integral, ∫-44∫15∫1ex2y2zdz dx dy
Q: (B): Find the unit vector perpendicular to the vectors: 3i - 4j+5k 4i + 5j-6k ;
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Q: Consider lim (x,y) → (0, 0) xy 20 X (see figure). 20 20 (a) Determine (if possible) the limit along…
A: Here to determine, lim(x,y)→(0,0)x2+y2xy
Q: Find the lengths of the sides of an isosceles triangle with a given perimeter if its area is to be…
A: Solution is given below:
Q: Q4: (chose one only) 3-x 1- f(x) = 2 x 2 a) Find limx→2+ f(x), limx→2- f(x) andf(2). b) Dose limx-2…
A: Since you have posted multiple questions i can do first question as per our company guidelines…
Q: Find the length of the following three-dimensional curv r(t) = (9+5t,3-2t,-1+2t), for 1sts6
A: To find the length of the given three dimensional curve.
Q: Let r(t) = (e²t, e−³,5t) Calculate the velocity vector and the acceleration vector at t = 0.
A: r(t) = ( e2t , e-3t , 5t ) given find velocity vector and acceleration vector velocity vector…
Q: In Exercises 37-42, use the Shell Method to find the volume obtained by rotating region A in Figure…
A: See this solution in below
Q: dy dx Q5: Find for the following functions: (2) y = tan³√√cot(7x);
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Q: (B): If A = 2i +3j - 4k; B = 3i-4j+5k and C=i+j-k, find: (ii) B.C (iii)A. (B+C)and (A + B).C (iv)…
A: Given: A→=2i+3j−4k;B→=3i−4j+5k and C→=i+j−k We know that x1i +y1j+z1k·x2i +y2j+z2k = x1x2+y1y2+z1z2
Q: 2. Find the equation of the line tangent to the circle x² + y² + 6x - 2y - 15 = 0 at the point…
A: Here the given circle is , x2+y2+6x-2y-15=0 We need to find the tangent to this circle at the point…
Q: Find f if f"(x) = 2 + cos(x), f(0) = -1, f(π/2) = 2. f(x) =
A: Find f if f"(x)= 2+cos(x), f(0)= -1 , f(π/2)= 2
Q: Calculate the distance between the point Q(3, 1, 7) and the plane 2x - 6y – z = 3. Don't use a…
A: We need to calculate the distance between the point Q3,1,7 and the plane 2x-6y-z=3 without using the…
Q: 11. f -dx 3x+1 +4x
A: these 2 questions are not related to each other so according to bartleby guidelines I need to solve…
Q: Q2/ A. Find the following limits. Answer four only. i. ii. iii. iv. V. lim x1 x-1 4x-x² lim X-4…
A: To evaluate the limit.
Q: A boat purchased for $25,000 depreciates exponentially. After one year, the car is valued at…
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Q: 7√2 2 0 x² 49-x² dxl
A: The given integral, ∫0722x249-x2dx
Q: Find a set of parametric equations for the line tangent to the space curve at point P. (Enter your…
A: We need to find parametric equation.
Q: Find S н - 2+ dx
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Q: Find f(145) (x) for f(x) = 83x¹0⁹. Simplify your answer completely. f (145) (x) =
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Q: Given the equation 5 sin 6xy = 3, evaluate dy Assume that the equation implicitly defines y as a…
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Q: Skill Building In Problems 13-24, use the graph on the right of the function f. 13. Is fincreasing…
A: Please see the answers below.
Q: Rewrite the expression In 3 + 5 ln x + 6 ln(x² + 4) as a single logarithm In A. Then the function A…
A: We know the property of logarithm that ln(a)+ln(b)= ln(ab) ...(1) And, pln(x)= lnxp .....(2)…
Q: f(t) = 4e-3t - sin 4t + cos 2t
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Q: 11, 0-20² 2. 3. चं 5. T S cos 2x dx sin(²³) cos²(:-) / dx 2x-1 4x dx dx 6. 7. 8. S [² (x² + 0²³) dx…
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Q: Q5: Find for the following functions: TTTTTT³ : (2) y tan³√cot(7x) : = (4) y = x sinh 2x-cosh 2x (3)…
A: Note:As per our guidelines we are supposed to answer only one question if there are multiple…
Q: 4. y = Ae bx are cosax + Bebx sinax, where a and b(lowercase) parameters. (not to be eliminated)
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Q: (B): Find the tangent equation to the curve y = sin² x at point x = 7.
A: I have stated the used formulas in the solution
Q: Find the general solution of the following differential equation. 64y" +80y + 25y = 0 NOTE: Use c₁…
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