1 Σ 6" - 5 n = 1 8

Q: Given f"(x) = 7x – 3 and f'(-2) = -6 and f(-2) = 6. Find f(4) %3D |

A: Here we will find f(4),

Q: Зx* у + tan y dy Given a first order differential equation dx Q3 x' +xsec? (a) Clarify the exactness…

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Q: If f is just that = e*[- sin(x + y) + cos(x +y)] and -e sin(x+y) which if the %3D ay following is…

A: On solving this we will get:- Option (A) is correct.

Q: Using (sin x) = cos x and (cos x) = – sin r dr dr Show that # (cot x) = - csc² x dr

A: We need to show that ddx(cot x) = -csc2 x Given ddx(sin x) = cos x and ddx(cos x) = -sin x

Q: Find div F and curl F if F(r, y, z) = xz°i+ 2y°x²j+ 6z²yk div F= 2° + 16 y' x + 12 z Y curl F=

A: Given F(x,y,z)=xz6i+2y8x2j+6z2ykTo find div F & curl F:

Q: Use the formula k(t) = |r(t) × r"(t)|| ||r(t)||° to find «(t). r(t) = 8 cos(7t)i+ 8 sin(7t)j + 3tk…

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Q: Find the equation of the tangent line in the given place. complete solution 1.) Tangent to the…

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Q: Given the equation z + 10z°y – 8y² + z* = 4 az Use implicit differentiation to find dz

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Q: dr2, dri r(t) - r2(t)] = r1(t) - r2(t) and dt dt dt dro dr.

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Q: 1 dx X +x13

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Q: S-2 ds (s-1)(s-5)(s+3)

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Q: e3t – 1 lim t0

A: Use l hospital rule for finding the limit.

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Q: Evaluate the following limits. If needed, enter oo for oo and -oo for – 0. V5 + 6x2 (a) lim 3+ 10x…

A: Use the substitution and then simplify the limit.

Q: d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: ay dy

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Q: Find the are lengtu of tue graph 10) of the fenetian y= x+5 over the imiterval [12, 14]. Anwens a) §…

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Q: S(1 + tanx)² dx

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Q: Find r'(t). r(t) = (tan (6t))i+t cos(t)j – Vik I| NOTE: Enter your answer in terms of i, j, and k.…

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Q: A ball is thrown into the air and its position is given by h(t) = - 4.3t2 + 41t + 15 where h is the…

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Q: x+1 8. -dx (x-1)

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: y=x 2 y = x+1

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Evaluate the defınite integral. 8 i + e¯´j+tk)dt 0, – (e-1 – 1) j+ k i-e'j+;k 8 (e* – 1) i – (e- –…

A: The given integral is: I=∫01e8ti+e-tj+tkdt   We know that; The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The…

Q: 26) find the mternel of convergenu of tue power Senies (x-6)*-1 и -) 6 onsurs : aj (6,l2) d) (-6,6)…

A: A detailed solution is given below.

Q: Find the indefinite integral. (a) / (2* + v#)dx (c) / 2x6 + x5 -dx x4 (4) [(4cs (xỉ + 5x + 4)dx (4…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: ; Test the following series whether it is convergent or divergent (show all your works) n2 +7 a) 2…

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Q: 7.372 The rate of change of the weight of a mouse, can be modeled by r(t) grams per week, where t t…

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Q: Problem 7. Solve the equation logx+log(x+1) = log12 and leave your answer in exact value.

A: Topic = Algebra x=3

Q: Evaluate the definite Integral. Use a graphing utility to vertfy your result. dx Step 1 To evaluate…

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Q: Find curl (8z i + 9x j + 10y k). curl(8z i + 9x j+ 10y k) Di +(i Dj +( )k

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Q: Evaluate the limit using L'Hospital's rule ez – 1 lim z+0 sin(82)

A: Here I have appended the formula used in the solution part.

Q: Determine whether the series converges absolutely or conditionally, or diverges. (-1)" + 1 n + 8 n =…

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Q: Evaluate the definite integral. i +e´j+tk )dt O e 7 – 1 e17 - (e-' – 1) + - (e~) - 1) j + k 17 O el7…

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Q: Show that the function f defined by (x, y) = (1, – 1) f(x, y) = 1² + y (x, y) # (1, –1) I + Y is not…

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Q: Find div F and curl F if F(x, y; z) = x°i – 7j+yzk. div F= curl F=

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Q: In(æ) -de (2)/ 1

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Q: `x² In x dx

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Q: Determine whether the following equation is separable. If so, solve the given initial value problem.…

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Q: Evaluate the definite integral. + ej+ dt - 1) i - (e" - 1) j +k O e? i+ (e-1-1) j+국k 2.

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Q: F'e) × r"(t)|| Use the formula x(t) = to find k(t). r(t) = 8 cos(7t)i + 8 sin(7t)j + 3tk K(t)

A: r(t)=8 cos7t i +8 sin7t j +3t kr'(t)=-56 sin7t i +56 cos7t j +3…

Q: Problem 3. A stone is dropped in a lake, creating a circular ripple that travels outward at a speed…

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Q: 8) Fiad the volume of the solid gonereted by revelving the regien beunded by tue graphs of equetians…

A: Given problem:- Find the volume of the solid generated by revolving the region bounded by the graphs…

Q: Consider the function f(x) = 5 – 4x² , – 4 < x < 2. - The absolute maximum value is and this occurs…

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Q: Зx* у + tan y dy Given a first order differential equation dx x³ +x sec? y (a) Clarify the exactness…

A: To solve the given differential equation

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

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Q: find the area of the region bounded by y=(x+2)^2-1, the x-axis, x=-1, and x=2.

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Q: Solve the differential equation dy tan y x Cos x 3 dx

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Q: Find the sum of the series. s 7(-1)"72n + 2n + 1(2n + 1)! 00 Σ n = 0

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Q: Find the curvature and the radius of curvature at the stated poin r(t) = 11 cos(t)i + 10…

A: Here we have r→(t)=11cost i +10sint j +10t k  at=π2 The formula for curvature is…

Q: Find (a) the critical numbers of f (if any) (b) the open intervals on which the function is…

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