Let f(x) = = 52 – 3 if a 4 - -6x+b if x > 4 If f(x) is a function which is continuous everywhere, then we must have b=

Q: If f(x) ƒ'(x) = ƒ'(4) = = 4 sinx + 4 cos x, then

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Q: Q2- By using Chain Rule, find əu/əx, əu/əy, du/əz at (x, y, z) = ("/4-¹/2, -¹/2) u = esin-¹p. p =…

A: By using Chain Rule, to find ∂u∂x, ∂u∂y, and ∂u∂z at x, y,z=π4, 12, -12.u=eqr sin-1 p, p=sin x, q=z2…

Q: Q3. Use the chain rule method to find dt If (z=x. y), where x = cos (t) and y=sin (t)

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Q: If a ball is thrown into the air with an initial velocity of 42 ft/s, its height in feet after t…

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Q: Consider the vectors: • V [2 1 -2] • w = [101] • π = [6 -3 -2] (a) Calculate projžū (b) Calculate…

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Q: How would the triangle be drawn for this problem ?

A: Given: In a baseball field, a drone is flying directly between the first and second base. Distance…

Q: 3. Consider f(x) defined as follows: f(x) = 5x² + 13x + 6 |x + 2| [4 − 3x] + x, 2 x<-2 x ≥ −2…

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Q: 4. x = y² +6, x = 2, y = 0, y = 1 rotated about the line y -3

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Q: Using the First Derivative Test, what are the local extrema for the function s(x) = − 3x³ + 10x² −…

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Q: B: Fit a second order polynomials to the data in the following: 5 6 12 X Y 1 4 3 8 4 10 61 13 70 10…

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Q: Multivariate Calculus

A: We have to find the region bounded by the curves:x+y=2 ,  x=0 , y=0.Here x+y=2⇒y=2-x⇒y=(2-x)2…

Q: v=(√2x-4)G

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Q: The graph below is the function f(x) -5-4 2 03 Find lim 24-1- Find lim z→-1+ da 14 Find lim 24-1 23…

A: According to the graph

Q: Does it mean that the limit of the function 2y + [[2-y]] / y^2 + y -2 as x approaches -2 from the…

A: limx→a+f(x) represents the Right hand limit )L.H.L)and  limx→a-f(x) represents the Left Hand limit…

Q: Identify and sketch the domain of f(x, y) = √4-x²-y In x

A: Given function : f(x,y)=4−x2−ylnx

Q: 2. In a factory, all employees work a basic week of 38 hours. Any overtime worked is paid for at…

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Q: Use the given graph to estimate the value of each derivative. (a) f(-3) (b) f'(-2) (c) f'(-1) y =…

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Q: Eliminate A and B from the relation y = Ae²+ Bxe²x

A: We are given  y = Ae2x + Bxe2x      y = (A+Bx) e2x     ... @ we have to eliminate A and B from @…

Q: Find the curvature of r(t) = (5t, t², t³) at the point (5, 1, 1). K=

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Q: Find the rule of a quadratic function whose graph has the given vertex and passes through the given…

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Q: lve (a) da 2y X x²

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Q: 2.) If x= 3, lim In(x+h)-In(x)

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Q: [200] 020 00 02

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Q: Exercise 3 nd the order of the following differential equations: a.) y" - 2(y")² = (y'-2y)³ d²y V…

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Q: Problem 4: Find lim 818 1 -2.3 + 1 2.3.4 + ... + 1 2.(n+1).(n+2),

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Q: Exponential and Log Derivatives "hat is the slope of the line tangent to the graph of y = 2 In(x) at…

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Q: Problem 2 A Classify the critical points of the following function (in other words say if they are…

A: The given function is: f(x,y)=x2+y2-2y

Q: Consider f(x) defined as follows: f(x) = 5x² + 13x + 6 |x + 2| [4 - 3x] + x, " x < -2 x ≥ −2…

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Q: se implicit differentiation to find the equation of the tangent line to the function defined…

A: Given x3-x2y5=-2,point (-1,1) The objective is to find the equation of the tangent line to the…

Q: Is the graph of r(x) = 4x³ - 2x² + 9x - 2 concave up or down at the point with x-coordinate -1?

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Q: sin cos 0 cos sin

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Q: If f(x) = = -¹, find lim f(x). 9 x4+∞

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Q: the axis of the parabola. y=x2−4x+5       Question content area bottom left Part 1 The vertex is…

A: We can find equation of parabola.

Q: Fit a second order polynomials to the data in the following: X Y 1 4 3 8 4 10 5 12 6 13 7 10 8 9 93…

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Q: 2. Use the different differentiation rules and formulas to determine the derivative of the following…

A: Derivative

Q: Q1- Find all the second-order partial derivatives of the function: f(x, y) = sinxy

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Q: B: use Lagrange interpolation formula to determine the relationship between the force and velocity…

A: We can solve it by Lagrange Interpolation Formula given below

Q: A company produces and sells 1440 tables each year. Each production run has a fixed cost of $200 and…

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Q: 2√x 1. y = 5√x 2. y = e²x+lnx

A: Basic identities of derivative are used after some manipulations.

Q: A mummy was recently discovered. It now contains 66.7% of its original Carbon 14. About how old is…

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Q: Decompose 2x + 5 2x2 - 11x +5

A: A detailed solution is given below.

Q: Solve the problem. dP =kP+N, where N is a constant representing the net The rate of growth of a…

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Q: Evaluate lim x-2+ 2x + [2x] x² + x − 2 2x + [2x] 2 x² + x - 2 and lim x

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Q: A = 2001 810 -536

A: We know that if det(A) =0 then matrix A is not invertible, Given A=200810-536

Q: Question Find the equation of the horizontal line that contains the point (–9, 1). Provide your…

A: We can find the answer in the below steps.

Q: Question 3 Identify the variable of integration in the given definite integral. m (11yv²vy + 8y) dy…

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Q: and the 1st derivative of x³ + y³ - 6xy = 0

A: Topic: - application of derivatives

Q: Evaluate lim x-2+ 2x + [2x] x² + x - 2 2x + [2x] 2 x² + x - 2 and lim x

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Q: Q2/ A: Find the Fourier Series of the function : f(x) = X + π if - n< X < n and f(x+2n) = f(x)

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Q: inverse function

A: Given, y=cos-1sin 6x