Determine R³(t) if R²' (t) = <2e²+-41, +/= 1+1) and R (2) = <3, -5,0).

Q: 9. Find the maximum value of the directional derivative of f (x, y) = x²y + √y at the point (2, 1)…

A: Since gradient of function gives the maximum rate of change of the function.And directional…

Q: (14) Give the appropriate form of the partial fraction decomposition. 2x+32 (x+1)(x+7)

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Q: K Find an equation of the tangent line to the curve y ex when x = -2.37. CIXA y= (Simplify your…

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Q: 8. y'=fln(y²¹) + 1²

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Q: Given that h(x) = f(g(x)), use the graphs of f(x) and g(x) to find h'(3). -0.5 [A] 0 3.5 3 2:5 2 1.5…

A: Given that h(x) = f(g(x)) The graph of f(x) and g(x) is given as

Q: Question Let h(x) = f(x)g(x). If f(x) = 4x² + 3x + 1 and g(x) = 3x² – 3x – 4, what is h' (−1)? Do…

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Q: How would you evaluate S tan 7x sec ³x dx? Choose the correct answer below. OA. Rewrite the power of…

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

Q: In the previous Problem Set question, we started looking at the position function s(t)st, the…

A: Consider the position function s(t)=e5tsin(7t)   Formula  v(t)=ddt(s(t)) Product rule of derivatives…

Q: Determine whether the MVT applies to the given f on the given interval. Explain. If so, find all c…

A: Given function  f(x)=x3,           [-1,8]

Q: Find the linearization. L(x) of f(x)=x² +1/x a+x= 1₁

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Q: 63-68 Find the slope of the tangent line to the given polar curve at the point specified by the…

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Q: rotate the point (2,8) by the (3/5,4/5) about the origin (0,0). (3/5,4/5) is on the unit circle.

A: Given data, Point A(2,8)

Q: Find the centroid of the region lying underneath the graph of the function f(x) = e over the…

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Q: Give the appropriate form of the partial fraction decomposition for the following function. 3x…

A: Topic -Partial fraction decomposition We are given, 3x(x-1)2(x2+3)

Q: Only

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Q: Find the solution of the given initial value problem: y (4) + 2y" + y = 9t + 10; y(0) = y'(0) = 0,…

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Q: Find the Laplace transform of the function 3, 0≤t< 2π { 2π <t<∞ NOTE: Express the answer in terms of…

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Q: ategration by parts formula and explain the e indefinite integrals by using the suggeste f6x 6x…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find ged(1326, 819) using the Euclidean algorithm.

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Q: Let f(x) f(g(x)) = g(f(x)) 30 C Question Help: - 4 Find the following functions. Simplify your…

A: Given query is to indicated composite function.

Q: The independent variable x is missing in the given differential equation. Proceed as in this example…

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Q: If lf Ŕ(t) = et cos tỉ – et sin tj Find the velocity and acceleration vectors.

A: To find the velocity and acceleration vectors for the given position function.

Q: Find the inverse transform of the given function of s. F (s) = 6s - 49 s2-8s +41 A) f (B) f C) f =…

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Q: Let y = f(x) = 6x³ + 13x - 13 and g the inverse function of f. Note that f(1) = 6. Find the value of…

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Q: 1. (a) (b) Find and sketch the domain of the function f(x, y) = = Show that x²y² lim (x,y) →(0,0)…

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Q: lim f(x) = H→ ∞ 1- x - 3x² 5+x³

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Q: Classify the following DE's as Exact, Non-exact, Homogeneous or Bernoulli. A: (-xysinx + 2ycosx) dx…

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Q: Consider the shape with vertices (1,3),(4,7),(0,10),(-3,5) translate the rectangle so (1,3) lies on…

A: We need to transform the coordinates.

Q: = 9,g(-1) = -7, and is h' (-1)?

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Q: eai coefficio 3. Find all the roots of the polynomial f(x) = 2x¹ + x³ +7x² + 4x - 4.

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Q: Please snow your answer to at least 4 decimal places. 4x Determine the gradient of f(x, y) = eª*…

A: Given, f(x,y) =e4xsin(4y)    Find gradient at (x,y)=(1,2)

Q: Using the Second Derivative Test, where applicable, find all the relative extrema of f(x) = 12x³ −…

A: Let's find relative extrema of given function.

Q: 6. Condense the logarithmic expression into a single logarithm. log(t)-2 log(w-1) + log(t + 1)

A: We can condense the logarithmic expression in the below steps.

Q: 1. Evaluate the following expressions. Round your answer to 4 decimal places. a) 16 17 b) log,8. 195

A: Need to evaluate the given logarithmic expression.

Q: Set up a double integral to find the volume of the solid region bounded by the graphs of the…

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Q: Determine if the improper integral is convergent or divergent, and calculate its value if it is…

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Q: You are I down ata map. Avector U with lul=0 10 points north and a vector v with IVI-3points…

A: To find the magnitude and direction of cross product.

Q: 3. y' = sin(t + y)

A: Y'=sin(t+y) dy/dt=sin(t+y)......1 Let  v=t+y  Differentiate with respect to t

Q: A current state has a population of 3500. With the rate of 0.23/year, what will be the population…

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Q: Question Let h(x) and g(x) O O O = -4x-2 -4 = f(x) g(x)' Select the correct answer below: where f(x)…

A: We know, ddx(u(x)v(x))=v(x)u'(x)-u(x)v'(x)v(x)2

Q: 4. Find the measurements of a box shipped via USPS that will maximize the volume in order to give…

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Q: By using the definition of the derivative, one can sin(x) - 1 x-x/2 2x - R Identify the correct…

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Q: Find the minimum distance from the point to the surface  z =    4 − 2x − 2y.  (Hint: To simplify…

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Q: Parameterize boundary of triangle (0,0),(5,0),(3,9)

A: We can parameterize the triangle in the below steps.

Q: d. y'= 1+y² 1+t² y(0) = -1

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Q: 1. Simplify the following expressions without the aid of a calculator. a) log, (81) b) log2 (2525) -…

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Q: 2. Separation of Variables Determine which of the following differential equations are separable. Do…

A: 1) y'=1+ydydx=1+ydy1+y=dx Therefore given differentiable function is variable separable.

Q: Let h(x) = f(g(x)). If ƒ(−4) = −3, ƒ' (−4) = −1, g(1) = −4, and g'(1) = 3, find h' (1). Do not…

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Q: Consider the function f (x, y) = = √x² + y² - 4 x - 1

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Q: What is t' (x) if t(x) = Select the correct answer below: = 80x5 .? ex O t'(x) O t'(x) = 80( -). ○…

A: Given query is to find the derivative of the function.