Let f(x) = 5x6 if x ≤7 -8x+b if x>7 If f(x) is a function which is continuous everywhere, then we must have b= Now for fun, try to graph f(x).

Q: Let C be the curve obtained by intersecting the two surfaces x³ + 2xy + yz = 13 and 3x² − yz = −5.…

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Q: 2x^2(y)+3xy^2−2x=−6  at the point (3,0)

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Q: (coth²(x))

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Q: Suppose f(x, y) = xe -8x²-8y² Answer the following. 1. Find the local maxima of f. List your answers…

A: Detailed solution is given below

Q: SX IF X <1 Let F(X) = (^(X-2) IF XZ1 a, Find Limx→1¹ and lim x⇒ F(x) b. does LIM X→1 f(x) exist? C,…

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Q: Plot the point -2,-2 given in polar coordinates, and find other polar coordinates (r,0) of the point…

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Q: Find the indefinite integral. (Use C for the constant of integration.) / (8 cos(x) + 7 sin(x)) dx

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Q: If z is a function of x and y satisfying the equation yzArctan (2x) - r²e² = y, find the following.…

A: Let's find partial derivative by using chain rule.

Q: For the graph shown below do the following. a. Find the zeros and state the multiplicity of each…

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Q: Select the graph that represents the point -2,- OA. Q OB. (a) What are the coordinates of the point…

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Q: EXERCISE 56 Evaluate each of the following limits. 1. lim x ln x. Ans. *0. 3. lim x csc 2x. 4. 2.…

A: 1) limx-0 xlnx 2) limx-infinity x sin(pi/x) 3) limx-0 x csc(2x). Repost the next questions.

Q: Sketch the region whose area is given by the definite integral. [*√16-x² dx N -2 y 15 10 5 y 4 3 2 2…

A: Area=8π     unit2

Q: verify that the function. solution to the differential and find the y=c₁e-x + C₂ e 2x is a equation:…

A: Topic = Differential equation

Q: Consider the function: f(x) = 2x² – 2x – 1 Recall that the definition of the derivative is: f(x…

A: Given Equation:- fx=2x2-2x-1

Q: For the part of the solution to the DE shown below, y ln x ln y dx + dy = 0 [y ln x lny dx + dy =…

A: The given part of the DE is ∫ln x dx+∫dyy lny=0 We have to find the next step of the DE

Q: The linear approximation at x = 0 to f(x) = sin(4x) is: L(x) =

A: n

Q: a lim x³²-x² X→ I X-1 b) lim X- UT 5 4-1 (2x-1) (3x²+2x-7)(x²³-9x)

A: SOLUTION-

Q: . y = sec(x)√1+cot² x csc³(x)

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Q: 0 ven ₁ = 10 9 -8 (:). -8 compute the cross products as listed. -5

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Q: 10. Suppose for a differentiable function g(x), we have X g'(x) = ( − 3)³ (5x – 6). Identify and…

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Q: II. For each of the following ellipses, find the center, principal axis, vertices, co - vertices,…

A: As per Bartleby guidelines we only give first question answers. Please repost for other parts.

Q: Given `y_(n+1) = 0.4 y_n + 6, \quad y_0 = 240 `y_17`

A: Given that yn+1=0.4yn+6, y0=240 We have to find the value of y17

Q: Determine whether the series converges. 5 sin² k k! (3) (4) k=1 4k-2k+6 18k+k-8 WI

A: Given series  (3) ∑k=1∞5sin2kk!   (4)∑n=1∞  4n2−2n+68n7+n−8

Q: Find the derivative of the function. y = sin²(x² + 7) y' =

A: Given, y= sin2(x2+7) Formula: sin2x = (1-cos2x)/2

Q: verify that the function y = C₁ x ² + C₂ x ³ is a the differential equation: solution to and 2 x ²y"…

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Q: Find the exact length of the curve. y = In(cos(x)), 0≤x≤ I x≤ 6

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Q: Find f'(− 3) if f(x) = 8 3x.

A: Given query is to find indicated derivative.

Q: dy dx. √sin(xy) + 1 0 JJ h soɔ (hx)soɔ h 7/1²

A: Let's evaluate integral by using Fubini's theorem.

Q: Find the linear approximation to f(x) = - 1 X close to 1 1.002 and then use that to approximate 1…

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Q: Find the GS of y" - y' - 12y = 0

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Q: Use a linear approximation to estimate (0.99

A: Linear approximation is given below

Q: Given that - 8i is a zero, factor the following polynomial function completely. Use the Conjugate…

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Q: 3) An oven is preheated and then remains at a constant temperature. A potato is placed in the oven…

A: Concept: Given the equation to represent (T) temperature at a given time t Putting the values of (T)…

Q: The charge for a taxi ride in New York City is $3.00 for the first 1/4 of a mile, and then $0.40 for…

A: cost of ride c=3+1.6(m-14)

Q: 5. y = cosh[tanh(sinh(x))] :

A: since you have posted multiple question i can do first question as per our company guidelines.…

Q: A construction worker pulls a five-meter plank up the side of a building under construction by means…

A: Topic- Application of derivatives. We are given, Worker pulls the rope to which plank is tied at a…

Q: Solve the following first order differential equations: 1.1 (x²y + xy-y)dx + (x²y-2x²)dy-0 by…

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Q: a. f(x)=3x+4 7. (fog)(x) 9. (f+g-h)(x) b. g(x)=2x-5 C. h(x)=x²-1 8. (goh)(0) 10. (h+h)(-2)

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Q: Consider the initial value problem Observe that, if n = 0 or 1, the Bernoulli equation is linear.…

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Q: (a) Find the critical numbers of F. (Enter your answers as a comma-separated list.) X= (b) Find the…

A: (a).Consider the following function:f(x) = (x-7).exDifferentiate 'f(x)' with respect to 'x' we…

Q: Suppose g(x, y) = x³ - 6xy + 6y². Answer the following. In each case give all three coordinates of…

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Q: Experiment 1: Slide the blue circle on the parabola to the point (-2, 4). 1A. Does the slope of the…

A: Here the parabola having the formula y=x2-x-2, we need to draw the tangent at the point (-2,4) to…

Q: Use an appropriate substitution to solve the equation Observe that, if n = 0 or 1, the Bernoulli…

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Q: II. For each of the following ellipses, find the center, principal axis, vertices, co- vertices,…

A: Concept: In mathematics, an ellipse is the location of points in a plane so that their separation…

Q: A weight of 1000 pounds is suspended from two cables as shown in the figure. What is the tension in…

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Q: 1. Iff(x) = -2x+1, evaluate the following for x: (A) f(x)=1 (B) f(x) = -5 (C) f(x)=8

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Q: Normalize the vector v₁ Resulting Unit Vector: 2).

A: Find the magnitude of the given vector and divide the vector with the magnitude

Q: 3. Determine if the following functions are one-one. Explain why. •f: R R f(x) = (x - 2)² ● f:R R…

A: one- one function :Let f be a function which is one one if        x1≠x2   ⇒  f(x1) ≠ fx2 for every…

Q: Find a polynomial with integer coefficients that satisfies the given conditions. R has degree 4 and…

A: We need to find polynomial.