6) Find the linear approximation to R(t) = VE at t=32 Use the linear approximation to approximate the value of V28 and V5 Compare the approximated values to the exact values.

Q: Calculate the first eight terms of the sequence of partial sums correct to four decimal places. E…

A: We can solve as follows

Q: II. MULTIPLE CHOICE: Choose the correct alternative that satisfies the given question. Write your…

A: We have to find correct option for the given questions.

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A: We have to solve k(t)

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A: Given that       r = 10 cost i + 8 sint j - k

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A:

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A:

Q: Given y = (x + 1)(x + 2)² Find: y O (z + 2)(3x – 4) O (2 – x)(3x – 4) - O (x – 2)(3x + 4) O (2 +…

A: Apply the product rule of differentiation f·g'=f'·g+f·g' to find the derivative of the given…

Q: Use the Comparison Test to determine whether the series is convergent or divergent. 00 ,7/8 n' n = 2…

A: The given series,    ∑n=2∞1n78-1

Q: /hat is the area of the region bounded by the graphs of æ = y³ – 2y and DA = (3x – x² )dx DA = (? –…

A: Topic:- application of integration

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A: Given query is to find the limit of the expression.

Q: .2 x dx 9 – 4x²

A:

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A:

Q: Find the standard equatron of the sphere with the given chara ct eristics center:(-1,7 9) radius: 6

A:

Q: 5 4 3 1 T1/2 3T/2 -1 -2 -3 -4 -5 The graph of the function f(x) given above for the interval a E [0,…

A:

Q: Given the function g(x) = 8x³ + 12x² – 48x, find the first derivative, g'(x). g'(x) = (x),6 Notice…

A:

Q: Find the derivative of the function f(x) = 4v3x² – x. 12х - 2 A. V3x2-1 6х - 2 бх — 1 C. V3x2 –1 E.…

A: To find the derivative of f(x)=43x2-x

Q: 3 da Evaluate a+2 A. 3 B. 2 С. 1 D. 0

A:

Q: Fod ble Jecond deriyalive of Hhe Aullowing funchon g lx) = Inca=43)

A: g(x)=ln(x2+3)

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A: Topic:- geometry

Q: Write the equation of the trigonometric graph. try y = sin)+O 5 4 3 37 5 2. 2. 2 -2

A: Given query is to find the equation if the graph.

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A:

Q: What is the differential equation whose solution represents the family y = Ae3x + Be 3x+Ce4x? %3D O…

A:

Q: Find the four second partial derivatives, Observe that the second mixed partials a z = 19xeY-10ye

A: We will differentiate partially with respect to x and y.

Q: k S = (d – 2)? where c and k are positive constants which depend on the quantity of smoke each stack…

A:

Q: Refer to the graph below. Find lim f(x). 3. 2- 1+ -5 4-3 -2 -1 -1+ 3. 4 5 x -2+ -3+ Does not exist 4…

A:

Q: (2x – 3y) dx + (2y – 3x) dy

A:

Q: Find the point S so that ray (PQ) and ray (RS) are each of the same vector where P = (2, 5), Q = (1,…

A:

Q: Consider the following. f(x) = x(x² – 11x + 35) x2 g(x) %D (a) Use a graphing utility to graph the…

A:

Q: Use Green's Theorem to evaluate the line integral. y2 dx + xy dy C: boundary of the region lying…

A: Given problem:-

Q: Use the following information to answer the question below. lim f(x) = 3 lim f(x) = ∞ lim f(x) = -3…

A: Information of the function is given, we have to find the required values

Q: Qu= O.4 log (E+0.44 435 %3D Qa - 0.249(log Ea)-O.I77 Q8= 0.227 (log E3)-0.839 Q3= rearange equations…

A:

Q: Find V· (V × F), if F(x, y, z) = 5e**i+ 5xe®j – 7ev³k. V· (V × F) =

A:

Q: Use Green's Theorem to evaluate the line integral (y - x)dx + (2x - y)dy for the given path. C: x =…

A:

Q: 1+ cx, if x 2 Given the function: f(x) = C - x, What should be the value of c so thatf is…

A:

Q: 4. Find the equation of the tangent line and normal line that passes through the circle (x – 2)² +…

A:

Q: What is the volume of the solid formed by revolving the region bounded by the graphs of x2 = 5y and…

A: To find the integral of volume of solid formed by revolving the given region.

Q: Peaive marima and, minima, 4 any tar the funchno If there is not an answers write N/A Wde ms wefs as…

A:

Q: ||r'(t) x r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). r(t) = 8 cos(8t)i+8 sin(8t)j+ 5tk…

A: The given formula is: κt=r't×r''tr't3 And rt=8cos8ti+8sin8tj+5tk

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

A:

Q: Find the derivative of the following equation x+3 x-4 (a-4)° 2x (x-4)² 7 (x-4) 2x-1 (x–4)°

A:

Q: Use the graph of the function f(x) shown below to evaluate lim f(x). x 3+ 3 2 3 O 3 O 1 O DNE 2.

A:

Q: Consider the following equations. f(y) %3D У(5 — у) g(y) = -y

A:

Q: Solve the initial value problemy-10y +50v-0 for y(0)-1 andy (0)-5. After getting the equation for…

A:

Q: 3. Suppose that the revenue in selling a tables is equal to 200x-0.25a2 dollars, and producing a…

A: topic - application of derivatives

Q: Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer…

A:

Q: ||r'(t) × r"(t)|| ||r"(t)||* Use the formula k(t) = to find k(t). r(t) = t²i + t°j %3D K(t) =

A: Given: r(t) = t2i +t5j Solution: r'(t) =ddtt2i+t5j =2t i +5t4j r"(t) =ddt2t i +5t4j= 2i + 20t3j

Q: Find div F and curl F if F(x, y, z) = xz°i+ 2y'x²j+ 2z²yk. %3D div F= curl F=

A:

Q: / Va2 – 1 ¢2 – 1 dx

A:

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: Here,  a→(t)=3t i^+6 sin(t)j^+cos(2t)k^⇒v→(t)=∫3t i^+6 sin(t)j^+cos(2t)k^dt⇒v→(t)=3t22 i^+6…

Q: Evaluate et-2 lim x→2 _x – 2 1 O +∞ O 1 O -00

A: Use l hospital rule for finding the correct option.