a. Consider the parabola f(x) = x² -4x + 3 i) Write the equation in vertex form. ii) Find the vertex and axis of symmetry. iii) Find the x-intercept and the y-intercept

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A: Given query is to find the area of the parallelogram.

Q: the Standard iom TocI. he standal the equation (Type an equation. Simplify your answer.) (-1,1) -4

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A: ∫5z3ezdzusing integration by part ∫fxgxdx=fx∫gxdx-∫dfx∫gxdxdxNow, fx=5z3,gx=ez∫5z3ezdz=5z3∫ezdz-∫d5z...

Q: QUESTION 10o Select each convergent series from the options below. No work required. 1 n=1 5 n=1

A: P-Test: The series ∑n=1∞1np converges if p>1 and diverges if p≤1 The series ∑n=1∞rn converges if ...

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A: we have to find the elasticity.

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A: To evaluate the given iterated integral.  

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A: Solution is written in below steps.

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Q: a. Consider the circle, x2 + 6x + y? + 18y + 89 = 0 i) Write the equation of the circle in standard ...

A: "Since you have asked multiple question, we will solve the first question for you. If you want any s...

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A: Integration by parts:∫u(x)v(x)dx=u(x)∫v(x)dx-∫du(x)dx∫v(x)dx

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A: F is exponential. 

Q: (1-cos 6x)dx 1+cos 6x c. tan3x – x+ C Perform the integration:S A. tanx – x + c B. -tanx – x+ C 3 3 ...

A: To find given integral.

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A: We know,  Range of sinx = [-1,1] for all real x. Range of ln(x)=-∞,∞ for all real x Range of a (x+a...

Q: What is the area bounded by the curve x² = -9y and the line y +1 = 0 ? A. 4 sq.units B. 2 sq.units c...

A: I am attaching image so that you understand each and every step.

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Q: Determine the open disk of convergence and radius of convergence of 2n (z – 1+ 2i)" -n + 1 n3D0 8.

A: Here we have to find the radius of convergence and open disk of convergence. 

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Q: If f(x) is continuous over an interval [a,b], and the function F(x) is defined by F(x) = [ f(t) dt, ...

A: This is a problem related to the trigonometric integral calculus. Based on the general fundamental t...

Q: dx Evaluate: S sin'x A. 3tanx с. tan?x + C tan x 1 + C tan 2x tanx + C tanx в. D. 2tan?x 3tan?x A C

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Q: Suppose that 8 J of work is needed to stretch a spring from its natural length of 40 cm to a length ...

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Q: Evaluate the integral. (Re du |u3- u?

A: Solution is written in below steps.

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Q: Use Lagrange multipliers to find the maximum and minimum values of the function f(x, y) = y² – x² su...

A: f(x,y)=y2-x2g(x,y)=14x2+y2-1=0∇f=-2x, 2y∇g=x2, 2ySet up:∇f=λ∇g and g(x,y)=02y(λ-1)=0-2x-λx2=0x24+y2=...

Q: S dx Evaluate: А. п B. VT c. VT3 в. D. еп A B C D

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Q: Find the area of the parallelogram that has u = 2i – 2j +k and v = j+ 3k as adjacent sides. NOTE: En...

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Q: 2. Solve the following differential equations. (a) y' = x2 - xy +1. (Hint: Consider the subsitution ...

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Q: perpendicular lines have the slope m1,m2 = 1 False O True

A: This is a problem related to the slope of the line which is perpendicular to existing line.

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A: I am attaching image so that you understand each and every step.

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A: ∫cos3xsinxdx  

Q: Suppose that f and g are integrable and that f (x) dx : :-1 | f(x). h(x) dx = 4 Odx = 5 Use the rule...

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Q: Find the area of the parallelogram that has u= 2i – 2j + k and v=j+3k as adjacent sides. NOTE: Enter...

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A: The objective is to evaluate the integral.

Q: Evaluate the sums. 6 a. (3 - k²) Σε. k=1 6 b. (k? – 5) k=1 > k(3k + 5) С. k=1

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A: We have to find the root of the given cubic equation using bisection method.

Q: Find the gradient of the function at the given point. f(x, y) = 5x + 3y2 + 5, (4, 1) Vf(4, 1) =

A: f(x,y)=5x+3y2+5 fx(x,y,z)=5fy(x,y,z)=3(2y)=6y∇f =fx(x,y,z) i +fy(x,y,z) j

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A: Use the definitions of improper integrals to write the improper integral in terms of limits.

Q: olve the following differential equations of 2 • dx+ 2(xe" – y)dy =0;

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