5.8 Evaluate n=1 2" -

Q: Find the exact length of the polar curve. r = 0, 0 < 0 < 37/2 12.47776

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Q: A. For each of the following functions, find the indicated derivative using the definition. 4. f(x)…

A: Let's find.

Q: A= 4 B=5 30 - 2 Find the 5 Only) following (chease A+ B (2) 3A -B A 2B (inverse) (leng th or…

A: Solving

Q: Give the curve r = 3 cos 0 a) Find the points on the given curve r = 3 cos 0 where the tangent line…

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Q: Use logarithmic differentiation to find dy/dx. (x + 1)(x - 7 (x - 1)(x + 7) x > 7 Step 1 The given…

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Q: 1. A function g is defined as 22 if a 1' g(x) Is it possible to find a value of the constant k that…

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Q: A population of 460 bacterta Is Introduced Into a culture and grows in number according to the…

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Q: a) Find the value of a such that the series 00 a E(-1)" is equal to . If it is not possible 2" n=0…

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Q: Calculate the derivative: d dx * ST (6t3 – 9t) dt = -

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Q: Let g(x) V1+ 8t dt. Use the Fundamental Theorem of Calculus to find g'(x). g'(z) =

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Q: Determine the convergence or divergence of the series. (If you need to use co or -00, enter INFINITY…

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Q: Estimate the instantaneous rate of change at x= 1 for Ax) = /x + 1. a) -2 b) -0.5 c) 0.5 d) 2

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Q: Find a particular solution of the indicated linear system that satisfies the initial conditions x,…

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Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

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Q: 1. Use implicit differentiation to find an equation of the tangent line to the hyperbola - * = 1 at…

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Q: The average rate of change of Ax) = x +x -x-1 over the interval o<xs1 is -2 1 O -1 2

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Q: Use the General Power Rule to find the derivative of the function. g(x) =    9 − 7x g'(x) =

A: We have to find g'(x) using the general power rule.

Q: 2-4x3 3. lim X→0- 5x²+3x³

A: To evaluate: limx→0-2-4x35x2+3x3

Q: 12. r(t) at cos 3ti + b sin³tj + c cos't k =

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Q: Evaluate A Se-* dx by Simpson's 1/3 rule with n=10, work for six digit

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Q: 3 ų (Vector Q.2 For the twJo Vectors: A=i-3j-2k B= 31 +5j +7K Find Ahe fallowing O BA Å+2B %3D…

A: Solution of question is written in below steps.

Q: Find Ax) if A1) =-5, and the tangent line at x has slope (3x- 1)e*-2*.

A: The tangent line at x has slope 3x-1e3x2-2x and f1=-e2

Q: Hw) Salvethe diffequ

A: We need to solve D.E.

Q: -2n f) S“ cos 2x dx g) S et² t dt h) S x sin(x²) dx

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Q: Find length of the curve described by the parametric equations x = T sin t, y = r cost, e <t< T. А.…

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Q: Find the the fo Howing differen equation general integration of tial xy'-y =xy? | %1

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Q: III. Graph the following functions: 4. y lIn(x-3) 5. y= In(x-1) 6. y= In Vx-1

A: Consider the functions 4.   y=|ln(x-3)|5.   y=lnx-126.   y=lnx-1

Q: 1) Find the exact length of the polar curve r = 2+2 cos 0. Show All Your Work!

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Q: Use the Root Test to determine the convergence or divergence of the series. (If you need to use co…

A: Root Test : Consider the positive term series ∑ an . Define,         L= limn→∞  ann= limn→∞ an1n ,…

Q: Consider the following. Function Point f(x) = arcsec 5x 4 (a) Find an equation of the tangent line…

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Q: 19. Suppose that the normal unit vector N of a surface S at z =f (x,y) is determined, how does the…

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Q: Date Name Written Homework 3.6 & 3.7 1) Solve a triangle ABC if a = 57.5, c = 49.8, A = 136°. Round…

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Q: Find the Maclaurin series for the given function.

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Q: Find an equation of the hyperbola having foci at (1,-2-/25) and (1, -2+25) and asymptotes at 3 r- 4.…

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Q: Find the slope of the tangent line to the graph of the function at the given point. g(x) = 14 – x;…

A: Use. Slope formula for finding the value

Q: To find f(x), let y = (x) and solve for x, y x - 4 Interchange x and y In the expression for X, Find…

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Q: The Mean Value Theorem states that if a function f is continuous on the closed interval [a,b] and…

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Q: T rsinx S"Stnx y dy dx 2 dx dy

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Q: Find an equation of the Ellipse that has Foci (-1,-2) & (7, -2) and vertex (8, -2). (a-3)2 (y+2)? 1…

A: We need to find equation of ellipse.

Q: Find the exact length of the curve. x = 8 + 12t2 y = 3 + 8t3 Osts 3

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Q: (a) 1+2+4+ 8+16 + 32 (b) -1+2- 4+8 – 16 +32 4 16 (c) 64 256 5

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Q: 55 Find the area of the surface generated by revolving x = 4/4-y, 0sys about the y-axis. 16 The area…

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Q: Verify that f has an inverse function. Then use the function f and the given real number a to find…

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Q: Determine the equation of the tangent to fr) = x + x at the point (1, 2). %3D O a) y = 3x - 1 %3D b)…

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Q: The term a29 of the sequence {a,} given by 4 7 10 13 4'5' 6'7 is 91 33 Select one: O True O False

A: We have to find a29 term.

Q: Illustrate the graph: A Y X 4. Prove whether the function f(x) = Vx – 2 is continuous interval [2,…

A: Given: f(x)=x-2 on interval [2,4]

Q: Find the slope of the graph of the function at the glven polnt. Use the derivative feature of a…

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Q: 2t 3t – 1 Verify the product law for differentiation, (AB)' = A'B + AB' where A(t) = 13 1 and 1-t…

A: To verify the product law for differentiation, AB'=A'B+AB' where, At=2t3t-1t31t and Bt=1-t1+t2t25t3.

Q: Use the Ratio Test or the Root Test to determine the convergence or divergence of the series. 1 1 1…

A: Given problem:-

Q: 15–18 Find the unit tangent vector T(t) at the point with the given value of the parameter t. 15.…

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