Consider the given function k(x) = x² + 12x+35 (a) Write the function in vertex form. (b) Identify the vertex. (c) Determine the x-intercept(s).

Q: The graph of f is shown in the figure to the right. Let A(x) = for f. Evaluate the following area…

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Q: Consider the following functions. f₁(x) = x, f₂(x) = x², f3(x) = 4x2x² g(x) = c₁f₁(x) + c₂f₂(x) +…

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Q: If f '(x) = 0 and f"(x) <0, then the point (x, f(x)) is a local minimum. a) always b) sometimes c)…

A: Please note that following the guidelines only one question is to solved.

Q: 2. J īdx 3 (x+2)+-(x+2)²

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Q: a) Evaluate [₁(x-3) (x-3)√√x+3dx

A: I have stated the used formula in the solution

Q: Compute the integral dx.

A: As we know that ∫xmdx=xm+1m+1+C see below the answer and calculation

Q: 3 2 X'+X +2x + 30 - 2 (22-3x+29 2) -dx

A: Let's integrate given integral.

Q: Evaluate [P r(t) = (t, sin(t), cos(t)), 0 ≤ t ≤ F. dr where F = (4z, - 3y, 2x), and C is given by

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Q: Use the Second Derivative Test to find the location of all local extrema in the interval (-2, 8) for…

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Q: Question Which of the following is a potential function f for F(x, y, z) = (2x cos(v2). -x²z sin(yz)…

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Q: Find ₁²² x²dA where R = {(x, y) | 4x² + 25y² < 100}

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. 8. f(x) = 2³3r² -…

A: In this question we have to find the absolute maximum and absolute minimum.

Q: Set up integrals To find the area of the regions between the curve of y=4 cos x and the x axis for 0…

A: The Solution is given below

Q: Find the derivative of the function g(x)=√t-sin (t) dt . Iv

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Q: 6 Find an equation of the line to the curve Y= √x that is parallel to the line 6x +Y=1. Y =

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Q: Sketch the plane curve represented by the vector-valued function and give the orientation of the…

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

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Q: Let r(t) = (et, t2 + 1, h(t)). If |r' (0)| = √2, which of the following is a possible h(t)? O sin(t)…

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Q: A graphing calculator is recommended. Consider the function below. (If an answer does not exist,…

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Q: Locate the absolute extrema of the function on the closed interval. In x, [1,4] 7x g(x) = minimum…

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Q: QUESTION 13 Is this true or false? The radius of convergence for Σ()" n=0 is R = Show why your…

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Q: 21) In a triangle ABC, B = 65°, C = 45° and a = 10. The measure of angle A is : a) O 90° b) O 80° c)…

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

Q: Find d [f₁z²dA where R = {(x, y) | 36x² +16y² ≤ 576}

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Q: Problem 7 Proof that if lim f(x) exists then it must be unique i.e., x→a if lim f(x) = L and lim…

A: In this question, we want to prove that if a limit of a function exist then it must be unique.

Q: ST ry² ds where C' is the right half of the circle x² + y² = 9 Evaluate

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Q: Please solve for part a of the problem provided in the photo below

A: Use partial derivative

Q: • Find f' (-1) for f(x) = (3x + 2)² in each of the following ways: • Create a table of secant slopes…

A: Solution is given below:

Q: 9) Find the min dimensions of a box that is 5000mL. Then find the min dimension of the lid and base.

A: To minimise dimensions minimise surface area  So differentiate surface area and equate to zero

Q: Consider the function below. (If an answer does not exist, enter DNE.) f(x) = x+6/(x^2+6)^1/2 Find…

A: See this solution in below

Q: Use the cross product to find the area of the parallelogram whose vertices are (0,0,0) , (0,2,1),…

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Q: 6. Consider the function f(x, y) = cot ¹(1+x) — 2e¹+³y If x = s²-t² and y = 3t+tan(1-s), use the…

A: Let's evaluate given partial derivative.

Q: (a) Use the Midpoint Rule with n = 6 to approximate integral Sc dx 8 x-6 x+8 Write your answer exact…

A: (a) From the given integral, the function is fx=x-6x+8, a=6, b=8 and n=6. Note that, the formula for…

Q: Problem 1 Find a linear differential equation with constant coefficients satisfied by e²x, e*, e³x,…

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Q: Use the rules for sums of powers of integers to compute the sum. 16 Σ k k=7

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Q: Let g(x) - 1² f(t) dt, where f is the function whose graph is shown. f S

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Q: Evaluate the indefinite integral. x² A -dx 1- x6

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Q: (a) [1 Show that the following equation represents a sphere, and find its center and radius. x² + y²…

A: As per our guidelines we only solve one question and rest of the question will be reposted.

Q: Use the graph below to write the quadratic function in vertex form. Be sure to use the equation…

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Q: Verify that the function satisfies the three hypotheses of Roll's Theorem on the given interval.…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: $3,200 is borrowed at 6.5% interest, find the amounts due at the end of 3 years if the interest is…

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Q: Consider the following graph on the interval - 360° < x < 45°: 360 -330-300 270-240 -210 -180 -150…

A: We have given a graph of function. And find to amplitude, period and function

Q: Use Green's Theorem to Calculate the Line Integral ſy²dx + x²dy, where c is the triangle o vertices…

A: Given that, the line integral is ∫y2dx+x2dy and the vertices of the triangle is 0,0,4,0 and 4,4. By…

Q: Find the largest interval centered about x = 0 for which the given initial-value problem has a…

A: We have to find the largest interval centered about x = 0 for which the given initial-value problem…

Q: Let R be the region bounded by y = x², x = 1, and y = 0. Use the shell method to find the volume of…

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Q: Find f(x)dx= 10 and ſ¹⁰ (6ƒ(x) — 10)dx = = = m m m

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Q: Evaluate 2 1 ² ₁² + √²³² - ²3/7 + 3x²³ - ²/3 d. X =)dx 3 X X 2 6.780 6.870 -6.870 -6.087 -0.687…

A: Given ∫12x3+x43-3x32+3x2-2xdx

Q: Set-up and evaluate the triple integral for the mass of the box 1≤x≤2, 1≤ y ≤16, 0≤z≤ with density…

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Q: Use the Midpoint Rule with n = 4 to approximate the integral. √x + 5dx = [Please enter your answer…

A: Here we have to use the midpoint rule

Q: c) [. The intersection of the sphere B and the xz-plane is (x - 2)² + (z + 1)² 2)² + (z + 1)² = 9.…

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Q: 4 Determine -2 u tv and Give a is i and v и So Keat orthogonal to ²-5²³ lutô| = |a²|+12²1…

A: Given the vectors u+v and u-v are orthogonal and  u+v=u+v To find u and v .