(b) : Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c guaranteed by the theorem. f(x)=x²-x, [1,5], f(c) = 12

Q: f(x) = (x-1)^3 (x-1) (x-2)

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Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary Integer…

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Q: Let r(t) = 21²i+tj+t²k. (a) Find the unit tangent vector T(t) and T(3). (b) Find the principal unit…

A: As per our guidelines we are supposed to answer only first 3 sub-parts. kindly repost others.…

Q: Find the equation of the langents to the graph y-x3 3x2-15x-20 at the points of the graph where the…

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Q: Find the critical points of the function f(x, y) = y² − x² + - a. [ b. I function f(x, y) = Find the…

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Q: Consider the following. y 4 3 Find its foci. 2 1 -1 -2 Find an equation of the ellipse. smaller…

A: we need to find the equation for ellipse

Q: find the derivative using implicit differentation

A: Apply derivative on both sides

Q: Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

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Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary Integer…

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Q: Find Unit Vector Find a vector (u) with magnitude 6 in the opposite direction as 7 = (-5, 4) Give…

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Q: A large snowball is melting so that its radius is decreasing at the rate of 4 inches per hour. How…

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Q: Find Magnitude and Direction (Angle) Giving the Vector Given the vector u = -47 +17, find the…

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Q: 20

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Q: b\ Fill the blanks 2/3 (1) Suppose you have a matrix x = [33], 13 4/5/61 2) Suppose you have a…

A: To fill in the blanks.a Suppose you hava a matrix x=12343456, then x...=35.b Suppose you hava a…

Q: Sketch the graph of the equation by point plotting. y = 5-x² -3 X y -2 0 2 3

A: Sketch the graph of the equation by point plotting

Q: Use Newton's method to approximate the given number correct to eight decimal places. √47 1.89969104…

A: Use Newton's method to approximate the given number correct to eight decimal places.476

Q: Let f(x) be defined by f(x) = x² sin(x) + x³. Find f'(1). Note: Your answer (if it's not an integer)…

A: Please see the below picture for detailed solution.

Q: Answer got marked wrong, please fix it.

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Q: Which one is correct for the sum of the geometric series O O O 9 10 11 5 17 10 6 5 O Divergent Σ1…

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Q: Evaluate the integral, which has irreducible quadratic factors. (Use C for the constant of…

A: We will find the integral.

Q: Find an equation of the line that passes through the points. (-2, 8), (1,5) Sketch the line. O No…

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Q: Find the equation of the tangent line to the curve y = 2x cos x at the point (₂ The equation of this…

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Q: I'm still confused on the position vector. The question is Let r(t) be the position vector…

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Q: Let f(x) be the following piecewise function x² + 1, 1 (x+1)² 2x-3 x²+1 f(x) = if x < -1 if -1 < x <…

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Q: Given f(x) = √√x and g(x) = x² - 9, evaluate each expression. (a) f(g(3)) (b) g(f(3)) (c) g(f(0))…

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Q: So if I write the position vector r(t)=OP=, is it correct? or does it has to be r(t)=<x,y,z

A: Solution is here

Q: Example 8 -[ If K= = A 12 9 12 15 3 0 2 } what is the value of k₁3 +k₁₁? B 9 C 3 D 5 E 18

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Q: 13 Given Sine= - 12/23 and Cos0>0. Find the remaining trig. values of 0. From Sec 5.3

A: sinθ = -1/5 cosθ&gt;0 here the quadrant given is 4th  because in 4th cosθ&gt;0 and sinθ&lt;0 now…

Q: y = ³/2, y = 8, x = 0

A: answer is in next step. please give a like .

Q: 13. A certain type of glass is such that a slab 1" thick absorbs one-quarter of the light which…

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Q: g(x) = cos ¹x+ x 1-x²

A: Topic = Derivative

Q: If a company spends r million dollars on research, it sales will be s million dollars, where r and s…

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Q: Identify the type of conic section whose equation is given. 2x2 = y2 + 2 parabola ellipse…

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Q: Use Newton's method to approximate the indicated root of the equation correct to six decimal places.…

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Q: Determine the Laplace Transform of the following functions: a. f(t) = 3te-5t cos(2t) b. g(t) = f(27)…

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Q: 19. A rectangular storage container is to have a volume of 44 m³ and has a lid. The length of its…

A: NOTE: Refresh your page if you can't see any equations. .   width of the storage container is W=x…

Q: Determine whether the series converges or diverges. n+5 Σ n = 11 (n + -6)5

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Q: Find the average rate of change of the function on the interval specified. g(x) = 6x3 − 7  on  [−3,…

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Q: Find the absolute minimum value of f(x) = 9x² - 5 x + 14 on the interval [0, ∞). Note: You need to…

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Q: Solve the equation for 8, where 0 ≤ 0 ≤ 2. (Enter your answers as a comma-separated list.) 2 cos²(e)…

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Q: Find the partial derivatives: af (x, y, z)/dx, f(x, y, z)/dy, df(x, y, z)/dz for the following three…

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Q: (1) Use the definition to prove that if x → 2 then (2x + 1)/x → 5/2.

A: xn→2 (2xn+1)xn

Q: Find the one-sided limit (if it exists). lim 11x² tan ex Step 1 The sign of the value of x² is…

A: To find the one‐sided limit if it exists.limx→12+ 11x2 tan πx

Q: Determine whether the equality is always true -10√x-9 (x-9)² f(x, y)d ydx = ₁ + f(x, y)dx dy. ²+9…

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Q: y = x², y = 4x - x²

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Q: 2 + y²

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Q: Find the limit (if it exists). (If the limit does not exist, enter DNE.) - (x² - -/-) lim

A: The given limit limx→0-x2-3x

Q: Differentiate d/dx  ∫ [cos(x), 0] t dt (using the Fundamental Theorem)

A: Differentiate d/dx  ∫ [cos(x), 0] t dt (using the Fundamental Theorem)

Q: work. a) ( i) Find the exact length of the curve 1 <2

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Q: 2e³y - ²x + 2y - 4

A: We will find the critical points.