Solve the following basic calculus problems: d а. cOS X dx b. [ydy 1 d? c. Show: dx dy d x++2y-x²)= x d. if dx df 1 df 1 -, find f(x, y) and x+y dy x+у

Q: The sum of two numbers is 25 and their difference is 7. Find the numbers.

A: Let x and y be two numbers . The sum of two numbers is 25.i.e. x+y=25 ...(1)The difference of two…

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Q: Question 1 1 -2 1. -1 1 2 -1 Let A and assume that 1 2 -1 0-1 -2 10 0 0 1 1 -1 0 0 0 0 0 0 1 -2 1 1.…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: SOLVE FOR THE LAPLACE TRANSFORM OF THE GIVEN EQUATION. 1.f(t) = te¯3t cos² 2t

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Q: . Write an expression equal to log3 (20) with as many logarithms as you want, but each log is of a…

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Q: 86. If f'(x) > 0 for all x and f"(x) < 0 for all xwhieh of the following could be a table of values…

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Q: 3. Armaan claims that the functions f(x) = 32x + 5 and g(x) = 32* + 8 have different instantaneous…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Use Green's Theorem to evaluate the line integral. v? dx + xy dy C: boundary of the region lying…

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Q: Below is a graph of f' (x), the derivative of f(x). A B D E When is: f(x) greatest? f(x) least? f…

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Q: Find div F and curl F if F(x, y, z) = 4y°z'i – 11x"2°j – 4xy°k. div F= curl F=

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Q: Examples: find the inverse laplace F(s) = 2s2 + 5 s3 +6s? + 5s -12

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Q: x² + xy? 2. (a) Evaluate the limit lim (x,y)→(1,2) x4 + 2y? or show that it does not exist. x2 + xy?…

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Q: Find the general solution of the given linear differential equations y" – 2y' – 8y = 24(x² + 1)e 4*…

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Q: Find curl (4z i + 5x j+ 2y k).

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Q: what is the equation of this picewise function? 10 2 10 -8 -4-2 2 46 8 10 -40 6,

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Q: Use Green's Theorem to evaluate the line integral (y – x)dx + (2x – y)dy for the given path. C: x =…

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Q: Using Euler's Method, approximate the initial value problem for various values of x given in the…

A: y'=9x2-4x+5,y(-1)=0,h=0.2 here, x0=-1,y0=0,h=0.2,xn=1 y'=9x2-4x+5 :.f(x,y)=9x2-4x+5 Modified Euler…

Q: Using Newton Raphson Methoc roots of the following equations. S solution via excel

A: The given equation is f(x)=x3+2x2-3x-1 find the derivative  f'(x)=3x2+4x-3 given xi=2 The formula…

Q: Find a 2 x 2 matrix A with integer entries where the characteristic polynomial |A – AI| is X² + 2A +…

A: Finding such a is equivalent to finding a 2 by 2 matrix with trace -2 and determinant 5. As in…

Q: -2 A = b, b2 1

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Q: Give the representation, equations and solution. Use elimination, comparison or substitution to…

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Q: The following data represents the growth of a bacteria population over time. Hours 1 12 Bacteria 600…

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Q: Determine the vector field of F. Fir y) - 4i - ?i

A: Given F=4i-2j the point is (4,-2)

Q: ) ور شم( موم 2 4-x 2 2 4-x 2 x++y¯+z° e - dz dy dx -2

A: To evaluate the below integral. ∫−22∫04−x2∫04−x2−y2e−x2+y2+z23/2dz dy dx

Q: 1 Give one example r that makes log. (r) rational but not an integer

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Q: Sketch exactly two full periods of y=-3/2 sin (x/2- pi/4). Indicate all the key points on the x-axis…

A: Given: y=-32 sin x2-π4 To sketch for two full periods.

Q: Use the Divergence Theorem to compute the net outward flux of the field F= (4x, y, - 2z) across the…

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Q: Are the vectors 16 + 16x – 12x2, linearly independent + - 12 – 12x – 12x2 and 18 + 18x – 3x2…

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Q: Solve the system of differential equations x' = 31x + 56y ly' 16x 29y - - x(0) = 7, y(0) = - 4 The…

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Q: Let D5 = (a,b). Compute the following: %3D b(a*b) bla'b) ab(a²b)

A: Use the definition of dihedral group.

Q: Select all that are True. A. O 2° = "the number of subsets of {1, 2, 3, 4, 5, 6} that don't contain…

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Q: John has 25 students in his class. He promised to bring lunch for them on Friday. Here is what the…

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Q: A few years back, Dave and Jana bought a new home. They borrowed $230,415 at an annual fixed rate of…

A: Solution:   The current time period is t=50 case 1: If Loan is not refinanced, No.of payments =…

Q: Assume that the function f : R → R is differentiable. 1. Show that the function u(x, y) = f(x+y)e¬¤…

A: (1) To show:  u(x,y)=f(x+y)e-x is a solution of ∂u∂x-∂u∂y=-u. (2) To find: A function f such that…

Q: 17. Evaluate L{y"(1) + 2y'(1) + y(1)}; y'(0) = -1, y(0) = 5. Let L {y()} = {s). A) (s°+2s+ 1)Y(s) –…

A: Here we use basic laplace transform

Q: (b) Show that any nonzero element of the ring Q[V2] = {a + bV2 | a, b e Q} is invertible, that is,…

A: (b) We have to show that any non zero element of the ring  ℚ[2] = a+b2 : a, b∈ℚ is invertible. (c)…

Q: 2. Show that the following graph is not planar. USM 1999 083 IVERS

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Q: 9. The graph of A sin(-3(x + 2)) -1 is obtained from the graph of y = sin(x) by: y = A) Shift left 6…

A: Here the graph of  y=12sin-3x+2-1 is oriented from the graph of y=sinx

Q: 2. Draw three different graph that has a Euler Circuit. (minimum of 5 vertices)

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Q: Use the statement, if p(E) = a/b, then o(E) = a:(b - a) and o(E') = (b- a):a, %3! to find the odds…

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Q: Determine the convergence or divergence of the series 1!/10 + 2!/10^3 + 3!/10^5 + ⋯ + n!/10^(2n-1)…

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Q: Let r be the second largest digit in your student ID. Let G and H be groups, and let p : G → H be an…

A: Given that G and H be groups and φ : G→H be an isomorphism. Also given g∈G have order r. To show: φg…

Q: Solve the equation x dy + y dx = 2x^2y dx. Select one: O a. In |x+y| = X^2 + c O b. In |xy| = x^2 +…

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Q: The line segment from (6,-2,3) to (-3,-2,1). 8 3 to 5 5 The line segment from 1,-- The position…

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Q: 22 +6 -9 -6 Find the slope. 3 3. 4. -1 3

A: We want to find slope of given graph.

Q: Solve AABC with the given measurements: a = 5cm, A= 50°, and C two decimal places. Show your…

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Q: Use Green's Theorem to evaluate the line integral. | (x - 4y) dx + (x + y) dy C: boundary of the…

A: The given integral is ∫Cx-4y dx+ x+y dy,  where C is the region bounded by x2+y2=1 and  x2+y2=16 To…

Q: Find an interval for a, the leading coefficient of the equation of a parabola, such that the…

A: A parabola is a curve equation in which a point on the curve is equidistant from both a fixed point…

Q: x sin x dr. 1+x2 7. Evaluate

A: We use residue theory to evaluate this integral. Also basic properties of definite integrals will be…

Q: 1. Consider the equation ODE dy dt y (1? – 9). %3D (a) Sketch the graph of dy as a function of y. dt…

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