Given the points G(1, –1, 3), H(-1, 2, 1), and K(4, 1, 1), find GH + GK ) × GH · ( GH + HK -23 31

Q: Ise substitution to find the Taylor series at x = 0 of the function 21 sin (- x). Vhat is the genera...

A: Topic:-  calculus

Q: Find the equation of the plane that contains the point (3, 2, 3) and the line  x = -4 +4t, y = -3t,...

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Q: Solve the limit:

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Q: Consider the function f(x)=1/x on the interval x>=1. find the Surface area and volume of the solid f...

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Q: Find the differential of each function. (a) y = tan(V5 dy = 1 - v2 (b) у 3 1 + y2 dy =

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Q: (b) y = e-u cos(u) dy = -e"sin(u) – e"cos( u) os u

A: The given function,  y=e-u cos(u)

Q: If a = [5,-2, 4], b [0, 2, -3], and c = [1, -2,1], find a xb.c -22 38 O(-2, –30, 10] 0.

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Q: Find the point (x,y), at which the graph of y = 6x + 6x - 5 has a horizontal tangent. 2 The function...

A: Topic = Derivative

Q: Determine whether the integral is convergent or divergent. The integral from -2 to 14, 7/(x+2)^1/4 d...

A: integration ∫-2147x+214dx

Q: dz Use the Chain Rule to find dt for z = x? + y? + xy, x = sin t, y = et.

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Q: 15 What is the exact value of tan (sinr) where r = 17? Provide your answer below:

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Q: Determine whether the improper integral converges and, if so, evaluate it. (Use symbolic notation an...

A: Topic = Integration

Q: A silver dollar is dropped from the top of a building that is 1317 feet tall. Use the position funct...

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Q: Find the missing values assuming continuously compounded interest. (Round your answers to two decima...

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Q: Consider the following function. x2 + 2x + 2 2 x3 3 (a) Find y' = f '(x). f'(x) = (b) Find the criti...

A: Given: - The function is, y=x33+x22-2x+2 To find: - (a) The derivative of the given function. (b) Th...

Q: Find the absolute maximum and the absolute minimum of f(x,y)= 3xy-3x-6y+1 on the closed triangular r...

A: Given:- The function is, f(x,y)=3xy-3x-6y+1on the closed triangular region whose vertices are (0,0),...

Q: 6. Find a set of parametric equations for the line tangent to the space curve at the given point. 2 ...

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Q: 75 ft A pole stands 75 feet tall, An angle 0 is formeđ when wires of various (engths of r feet are a...

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Q: dx 3. S xVx-8 4. S-5 cos r sin 2r dr

A: ∫1x2+a2 dx =12atan-1xa+C ∫un du = un+1n+1+C

Q: Does the parabola y = 3x - 26x + 4 have a tangent whose slope is - 2? If so, find an equation for th...

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Q: Find the minimum and maximum values of the function y = 2x-8x +7 on the interval [0, 5] by comparing...

A: Given that the function is        y = 2x2 - 8x + 7 on the interval [0,5] .

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.

Q: The number x of printer cartridges that a store will sell per week and their price p (in dollars) ar...

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Q: Write the equation of the sphere centered at (5, – 2, 4) with radius 3.

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Q: Find the differential of each function. (a) y = etan(nt) dy = (b) y = V4 + In(z) dy =

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Q: Suppose it is known that for a given differentiable function y = f(æ), its local linearization at th...

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Q: S(x) 3

A: The objective is to find the limit.

Q: Given the triangle below, find the angle 0. 15 10

A: Given that:                          

Q: The measure of each interior angle of a regular hexagon is

A: Measure of interior angle of regular hexagon

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the...

A: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the...

Q: cos 30 de

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Q: Suppose that lim (x,y)→(3,1) f(x,y) = 6. What can you say about the value of f (3,1)? What if f is c...

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Q: Find the average velocity over the interval [1,4] Find the average velocity over the interval [1,1 +...

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Q: Find equations of all lines having slope - 1 that are tangent to the curve y = x-8 Select the correc...

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Q: Without using a calculator, find the exact value of each: i. sin-1(sin)) =

A: topic- inverse trigonometric functions sin(π+θ)=-sin(θ)sin-1(-x)=-sin-1(x)

Q: Question Select your answer. 3, Given f(x) : if I< -2 if – 2<a < 8 , estimate -2 I +3, if lim f(x). ...

A: Topic =Limits

Q: (х + 3)2 dx. J V40 – 6x - x²

A: Evaluate ∫x+3240-6x-x2dx=?

Q: Let f(z) = |r - 5|. Evaluate the following limits. S(z) - f(5) lim Z-5 エー5. f(z) - f(5) lim Z-15 I -...

A: Given function f(x)=x-5 use the concept  for h&gt;0limx→a- f(x)=limh→0f(a-h)limx→a+ f(x)=limh→0f(a+h...

Q: Use implicit differentiation to find y' and then evaluate y' at (3,0). 9 eY =x2 -y? %3D y' =] y'l(3....

A: topic - implicit differentiation

Q: f(x) (x-1)(x-4). %3D x+4

A: Topic = Functions

Q: hi

A: 1232Now,32 = 2×2×2×2×2 =4×4×232 = 4×4×2 = 42

Q: a power series. Use the 2n +1 Integrate the function as 00 E(- 1)". Maclaurin series sin x= (2n +1)!...

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Q: Use the Integral Test to determine whether the infinite series is convergent. n2 Σ n=19 (n³ + 3)7 To...

A: ∑n=19∞n2n3+372We need to find the given series converges or diverges

Q: lim (3+ 2)

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Q: Find the initial velocity such that the particle will have the same position at t-4s a. and t- Os. b...

A: Follow the procedure given. 

Q: 1+x2+y2 Determine the set of points at which the function F(x, y) = is continuous. 1-x2-y2

A: In this we have to check Discontinuity of equation. 

Q: The graph of fis given. State the numbers at which f is not differentiable. (Enter your answers as a...

A: If there is a sharp point at x=a on the graph , then function is not differentiable at x=a. If funct...

Q: Find the tangent line to y = x -x+7 at x = 7. ,2 The tangent line to y = Vx -x + 7 at x = 7 is y =

A: We have to find tangent line

Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region a...

A: Given:       y = √(4-x2 )

Q: Given the side length b = 9 and the angle B = 43° on the triangle below, find the lengths of a and c...

A: Given that: