Find the absolute minimum and maximum value for the function on the given interval f (x) = x – 3x2 + 1, [-}, 4]

Q: Find r'(t). r(t) = (tan-(7t))i+t cos(t)j – Vēk

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A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

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A: Given: Fx,y,z=xz6i+2y8x2j+6z2yk

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A: Solution is given below:

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A: As you have asked multiple subparts so I have answered first three subparts as per the guidelines.

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Q: dx sinxtanx

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Q: Find div F and curl F if F(x, y, 2) = 17y*z*i – 3a*2®j – 3ry®k. div F= curl F=

A: Divergence of F: ∇·F=i→∂∂x+j→∂∂y+k→∂∂z.i→17y4z4-j→3x3z6-k→3xy6 ∇·F=∂∂x17y4z4+∂∂y-3x3z6+∂∂z-3xy6…

Q: 8. A 25-ft ladder is placed against a building resting on a banana peel. The base of the ladder is…

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Q: 1. Find fa(x, y) and fy(x, y) given f(x, y) = (csc y) Arcsin(r2).

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A: First frame the equation then verify all the given option.

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A: Topic = Derivative

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A: Partially Differentiate with respect to y

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A: We can solve the answer using the properties of definite integral as below.

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A: We have to find the angle

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Q: Find V · (V × F), if F(x, y, z) = 3e"*i+3.xe"j – 8ev²k. V ·(V × F)

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Q: Find r'(t). r(t) = (tan-(11t))i+t cos(t)j – Vik

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Q: e3t – 1 lim t0

A: Use l hospital rule for finding the limit.

Q: Find div F and curl F if F(x, y, z) = 17y*z*i – 3x'2ºj – 3ry®k. div F= curl F=

A: Let's find.

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A: As per guidelines if multiple questions are posted we are allowed to solve only 1st question...…

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

Q: Evaluate the definite integral. ell! i + e¯'j + t k )dt O ell – 1 (e-1 – 1) - (ell – 1) i – (e-1 –…

A: The given integral is: I=∫01e11ti+e-tj+tkdt   We know that; The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The…

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…

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Q: Example 22 Find the eccentricity and directrices of the hyperbola given x? y? 1 9 16 Sketch the…

A: Given: x29-y216=1

Q: 10 %3D1

A: Formula Given

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A: We will find the coordinates in polar form.

Q: 1. Sam throws a stone into a river. This caused ripples in the form of concentric circles. The…

A: Given problem:- Sam throws a stone into a river. This caused ripples in the form of concentric…

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A: Integration are simplyfied..

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Q: pind tue indefinete integral S In(s-1) ds

A: ∫ slns-1dsLet u=s-1=∫u+1lnudu=lnuu22+u-∫12u+2du=lnuu22+u-u24+uSubstitute back…

Q: 4- to --6 -5 -4 -3 -2 -1 5- ver which interval of z values is f'> 0? о (2, о) O 12, 0) 0(- 00, 2)…

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