9 8- 7 16 1 A 3 يها 2 1 If f(x) f'(3) = = g(x) g(x) h(x)' 2 3 x-values then 5 4 يها 2 1 h(x) 1 2 3 x-values

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

A: Given vector:- rt=2ti+etj+e-tk

Q: Solve the initial value problem y" + 4y + 4y = 32e²; y(0)=-1, y'(0) = 14. +Set →→ (Answer: Y =…

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Q: Which one of the following could be the graph of the polar function r = sin 30 ? 1. 011 2.

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Q: If f(8)=4, f'(8)=-5, g(8)=-3, and g'(8)=1 and h(x)=6f(x)-2g(x) find h'(8)   a) -32 b) -114 c) 0…

A: h(x)=6f(x)-2g(x) h'(x)=6f'(x)-2g'(x)

Q: did

A: Yes, you are right there is some mistake in part e. so, I am rectifying it in next step. Sorry for…

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Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) =…

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Q: a) y = cos 2x on [0,1] b) x= on [1,10]

A: 6) a) y=cos(2x) on [0,π] the length of the curve is given by  L=∫ab(1+f'(x)2) dx here f(x)=cos(2x)…

Q: The line normal to the graph of f at the point (1,2) passes through the point (-1,1).  Which of the…

A: Topic = Functions

Q: Find a Cartesian equation for the curve given by the polar equation r = 6 cos 0.

A: as per the roj we can only answer the first question and rest can be reposted.

Q: The shaded region in D = 4 cos and lies inside the polar curve r outside the polar curve r = cos 0.…

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Q: Sketch the plane curve. r(t)=3ti-tj, [0, 3] y 2 Find its length over the given interval. 6 6 8 8 10…

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Q: d²y(t) dt2 dy(s, t) Differential Equations + y(t) dy(t) — 2y(t) = 4x(t) - y(s, t) = dx(s, t) Linear…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Scientists can determine the age of ancient objects by the method of radiocarbon dating. The…

A: given half life thalf life = 5730 years      law of decay x = x0e-ktk = constant x = radioactivity…

Q: 4 Let f(x)=x²-3x-2380, x>0.75. Find the value of df-1 At x = 0, dx (Type an exact answer in…

A: Given function:- fx=x4-3x-2380

Q: y X

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Q: y = 5x³

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Q: Evaluate the definite integral. 6 L₁³25 1 25+ (x+4)² dx

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Q: If it is exact find a function F(x, y) whose differential, dF(x, y) gives the differential equation.…

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Q: Find an equation of the tangent line to the curve at the point (1, 1). y In(xex*) y =

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Q: Kindly help me solve this question,show full and clean solution thank you.. Note: Lesson about…

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Q: Find the second derivative of the function f(t)= t³sect. Of"(t)= t³sect(20+tsect+10ttant+ftan²t)…

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Q: d'T At a certain moment, the temperature in a snake cage satisfies = 0.008 °C/s. Estimate the rise…

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Q: For each function in Exercises 7-28, (a) give the coordinates of any critical points and classify…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: Evaluate. da [3.sin x] O x 3-¹ (sin x + cos x) O 3 In 3 cos x ● O 3. cos x 3 cos x + 3* .

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Q: 16. f(x) = x² - 2x³; [-2,2]

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Q: Write the particular solution of the first order linear differential equation dy + (ytanx - cosx)dx…

A: We need to solve D.E.

Q: a. The graph in the accompanying figure is made of line segments joined end to end. At which points…

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Q: Find a vector orthogonal to both (2,3,0) and to (0,3,4) of the form. 41,0, 07 for olmas

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Q: Consider the function of two variables f(x, y) = 3x³9x + y² + 4y + 6 (a) Find all the critical…

A: Consider the function of two variables fx, y=3x3-9x+y2+4y+6 a To find all the critical points of fx,…

Q: A conical tank (with vertex down) is 14 feet across the top and 20 feet deep. If water is flowing…

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Q: 34. f(x) = x² + 250 X (0, 0)

A: 34) f(x) = x2 + 250xfor find extrema   f'(x) = 0 &for minima f''(x) >0 for minima f''(x)…

Q: Provide the definition of matrix equivalence and explain the relationship of this notion to matrir…

A: To give the definition of matrix equivalence.   T:V→W

Q: What is the angle a= (-1₁8-4) and b = (2₁-5₁10) Angle - (radians) in radians between the vector-

A: Given query is to find the angle between the vectors.

Q: Find Vectors and Perform Vector Operations in R³ Vector 7=(2, 0, − 1) has initial point (-9, 7, 3).…

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Q: True or false: the limit as x approaches infinity of (x^2-x) =0

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Q: Differentiate the following. (a) y = sin(x4) (b) y = sin(x) Solution (a) If y = sin(x4), then the…

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Q: 23-24 Find the local maximum and minimum values of f using both the First and Second Derivative…

A: To find the local maximum and minimum values of f by using both the First and Second Derivative…

Q: Find the constant of integration of the first order linear differential equation ydx + (1 + 2y^2)xdy…

A: Let's solve given diffential equation.

Q: y-values 9 8+ 7+ 6- 4 3- 2 1 2 3 x-values 4 5 y-values 4- 3 2- 14 h(x) 1 2 3 x-values 5

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Q: Find the derivative of the function. Simplify if possible. y = arccos (e³x) y' =

A: Solution : Given that

Q: 1. 2. y"" +3y" +4y +12y = 8cos2x - 16sin2x y" - y'= -2(1+x) +4e* -6e-* +96e³x

A: Disclaimer:  “Since you have asked multiple question, we will solve the first question for you. If…

Q: Find r(t). u(t). r(t) = (7t − 8)i + t³j+ u(t) = t²i - 9j + t³k r(t) u(t): Is the result a…

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Q: A point P is given in Cartesian coordinates by P(1,1). Find polar coordinates (r, 0) of this point…

A: NOTE: Refresh your page if you can't see any equations. . the given point P is

Q: Consider following ODES: 1)4y" +12y' +13y=0,2 a) Find characteristic equation ar

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Q: Find the GS for y" - y = exe-x

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Q: Find the average value of the function over the given interval. (Round your answer to three decimal…

A: We need to find out the average value of the function.

Q: Which one of the following shaded-regions in the plane consists of all points whose polar…

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Q: Find the interval(s) on which f(x) = |x² - 9| is differentiable. Enter your answer using interval…

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one…

Q: Complete the description of the plecewise function graphed below. ● ***** ( f(0) = { { O AF Question…

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