(a) Find the equation of the secant line joining the points (-1, –4), and (3, 0). y= (x+1) - 4 (b) Use the Mean Value Theorem to determine a point c in the interval (-1, 3) such that the tangent line at c is parallel to the secant line. C = 1 (c) Find the equation of the tangent line through c. (d) Use a graphing utility to graph f, the secant line, and the tangent line. 12 14 2 -21 -2

Q: Differential Equation : Linear Differential Equation of Order c) #1 only (U can answer others thanks

A: Topic:- differential equations

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A: Given that: ∑k=1∞4k+27k-1

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Q: arctan dx

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Q: gent subsequer O an = (-2)" O an = 1+ (-1)" · 10(-1)"-n n sin () %3D O an = O an = 1+2· (-1)"

A:

Q: The ideal gas law PV = nRT gives a relationship between the pressure P in pascals (you can read abou...

A: Given: The ideal gas lawPV = nRTP : pressure                           variableV : Volume           ...

Q: 0.9012 82 82 82...

A:

Q: The measure of the supplement of a 71° angle is (Simplify your answer. Type an integer or a decimal....

A: Supplementary angles sum =180° ⇒180° - 71°=109°  

Q: 1. Find the length of the curve r(t) = (sin 2t, cos 2t) from t 0 to t = 2n. %3D 2. Find the length o...

A: As we know that, The expression for the length of vector-valued curve is: L=∫abx't2+y't2dt   1). Giv...

Q: ) Sketch the region enclosed by the given curves and find its area. y = -x² +4x, y=x² – 2x

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Q: 8. y= sec® (e-sin?x) |

A:

Q: 6 and its graph, use the graph to determine the following. r(x) 10 하 6 4 2 -4 -3 -2 -1 -2 1 2 3 4 -8...

A: where f'(x) is positive f(x) will increase and f'(x) is negative then f will decrease , observe the ...

Q: Consider the following. y = 2x5 + 5x* – 10 (a) Find the critical values of the function. (Enter your...

A: The given function is: y=2x5+5x4-10

Q: Use substitution to find the Taylor series at x = 0 of the function 15 sin (-x). ... What is the gen...

A: This question is based on Taylor series expansion of sinx .

Q: Use the difference an+1 a, to show that the sequence {n - 3"+∞ Sn=1 is strictly increasing or strict...

A: Calculus  mathematics sequence 

Q: Calculate the first four terms of the sequence, starting withn = 1. bj = 2 1 b, = bn-1 + bn-1 (Give ...

A: b1=2bn=bn-1+1bn-1

Q: 2. SS y' e ř drdy D: x=0, y=l,y= 2

A: Given: I=∫∫Dy2e-xy2dxdy And D: x=0, y=1, y=x2 We know that; ∫eax+bdx=eax+ba+C And ∫a·fxdx=a·∫fxdx, w...

Q: A robot arm joint moves in an elliptical path (horizontal major axis 8.0 cm, minor axis dy 4.0 cm, c...

A:

Q: Write the first five terms of the sequence: {Vn² +n – n}, n=1 Determine whether the sequence converg...

A: given sequence n2+n-n1∞  

Q: Find f-(x, y, z) in the function f(x, y, z) = a?y*z + ay +? +1. %3D A. fa(x, Y, z) = 4x²y°z* + x %3D...

A:

Q: 2y" – 3y" – 3y' + 2y = (e" + e¬²)²

A:

Q: Find the cross product ax b: a=(2, – 1, 2), b=<0, 4, 5)

A: Given that: a=&lt;2, -1, 2&gt;b=&lt;0, 4, 5&gt;

Q: dx x² Vx² +9

A: Given that a integration of 1/(x2√x2+9). We know that Integration power rule is given  as - integrat...

Q: y" + y' + 7Y e (sin 3x - cos 3x) (undetermined coefficients)

A: Given

Q: (a) Find the series' radius and interval of convergence. Find the values of x for which the series c...

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Q: Rewrite the integral in the 5 other orders. Explain your answers. 2 4-y2 f(x, y, z) dz dy dx

A: The given integral is ∫x=0x=1∫y=2xy=2∫z=0z=4-y2fx,y,z dzdydx. The domain of integral is R=x,y,z: 0≤x...

Q: Calculate the Taylor polynomials T2(x) and T3(x) centered at x = a for f(x) = 18 sin(x), a = . %3D (...

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Q: Evaluate the integral. dx (х — 4)(х — 8) (Use symbolic notation and fractions where needed. Use C fo...

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Q: If F(x) = f(g(x)), where f(−1) = 5, f '(−1) = 2, f '(−3) = 3, g(−3) = −1, and g'(−3) = 6, fin...

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Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

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Q: Find the x vals of all pnts where the function over the given interval has any relative extrema & fi...

A: The given function,    f(x)=7sinπx ; 0&lt;x&lt;2π

Q: (b) (x² + xy) = y² y = 1 when x = 2 dx dy (c) - y = e* sin(2x) y = 1 when x = 0 |

A: Given : (b)  x2+xy dydx=y2  ,         y = 1 when x = 2   which is y2=1 (c)   dydx-y= ex sin2x ,     ...

Q: Let f(x, y)= Jxy +x+xcos y. (a) Find fy - ở² f_ (b) Find дхду

A: f(x,y)=xy+x+x cos y

Q: Solve the following using a +/- table, making all of your thinking visible (r-2) (x+1) (4-x)(x+5) > ...

A: Find your answer below 

Q: Question Select your answer. 1, T - 1, if a > 0 if z < 0 Given f(x) = , estimate lim f(x). does not ...

A:

Q: Consider the differential equation = (3 - y)cos x. Let y = f(x) be the particular solution to the di...

A: The given differential equation is: dydx=3-ycos(x)

Q: ydx + x(Inx - lIny - 1) dy = 0, when x = 1, y = e %3D

A: Given :     ydx+xlnx-lny-1dy=0,        when x = 1 , y = e that means y1=e

Q: • What restriction (on x or y) does dy have? What dx point (x, y) does this correspond to? • Find th...

A: According to our policies we are allowed to answer only one question at a time. If you want solution...

Q: 4. How many solutions does the following system of equations have? x - 3y + z = 2 3x - 4y+ z =0 2y -...

A: Follow the procedure given below.

Q: 00 n Does the series (-1)"n*=| converge absolutely, converge conditionally, or diverge? n = 1 Choose...

A:

Q: Determine convergence or divergence by any method. 00 (-1)"n n=0 Vn2 + 9 The series diverges. conver...

A: The given series,       ∑n=0∞(-1)nnn2+9

Q: rsin 28x /ī+ t² dt and If f (x) = So g (y) = ' f (x) dæ., what is g" (6s )? 168

A:

Q: Answer the following True or False: If g(x) is the inverse of a differentiable function f(x) with de...

A: Find your answer below 

Q: 3. Complete the table for the function: y 21 Xy a 0 b 4 C 6 a= b= 2.

A: Topic = Function a=2 b=4 c=5

Q: You are designing a poster which has a border around th printed portion. The border is 2 inches wide...

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Q: Solve eX =9 for x. ... The solution is x (Type an integer or decimal rounded to four decimal places ...

A: Consider  ex=9

Q: 4. y=ysin 2xcos 5x + 3

A: Find your answer below 

Q: Consider the following. y y = fix) 4 (a) By reading values from the given graph of f, use five recta...

A:

Q: Let f(x, y)= Jxy +x+xcosy. (a) Find fxy-

A:

Q: Consider the following function. +] - 2x + 2 3 2 (a) Find y'-f"(x). "(x) = (b) Find the critical val...

A: Topic = Derivative As per guidelines , At  a time only three sub-parts can be answered.