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Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 3 lim 4 + 6A

A: We need to evaluate the value of given limit

Q: Assume a substance has a half-life of 11 years and the initial amount is 133 grams.How much remains ...

A: The amount left after t years can be calculated as

Q: Find the total area of the shaded region shown to the right given by the curve y = 4( sin x)/1+ cos ...

A: Given:

Q: In Exercises 25 and 26, find (a) the area of the parallelogram determined by vectors u and v and (b)...

A:

Q: Prove the following:  1. if ax=a for some number a≠0, then x=1

A: Prove that, if ax = a for some number a ≠ 0, then x = 1.It is given that, a is a nonzero real  numbe...

Q: Assume a substance has a half-life of 11 years and the initial amount is 133 grams.How long will it ...

A: If A0 is initial amount present and T is half -life of the substance. Then the amount of substance r...

Q: Evaluate the integral and interpret it as a difference of areas.  Illustrate with a sketch. (integra...

A: Sketch and interpret it as difference of areas.Sketch the graph.

Q: Use the four-step process to find f' (x) and then find f'(1), f'(4), and f'(8). f(x) = 2x² – x -3 f'...

A:

Q: Solve the equation for all solutions in the interval [0,2π). sin(3x)=−√3/2 Express each solution in ...

A: Find 3x using sin inverse. 

Q: Can I get help step by step with this problem please?

A: Given:

Q: Find the limit, if it exists.

A: Given expression is,

Q: Skill Practice 5 Solve the inequality. Al

A: Given:

Q: 8x sec2(x) on the interval [0, T/4]. Calculate the average value of f(x)

A: According to the given information it is required to calculate the average value of the function

Q: Find an equation for the circle of curvature of the curve r(t) = (2 ln t)i - 3t + (1/t)4j, e-2 <=...

A: Consider the given curve as,

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

A: We need to find the volume V of the solid obtained by rotating the region bounded by the given curve...

Q: Show that the line in which the planes x + 2y - 2z = 5 and 5x - 2y - z = 0 intersect is parallel to ...

A: Find the vectors normal to the planes x + 2y - 2z = 5 and 5x - 2y - z = 0.

Q: For Exercises 17 and 18, find the acute angle between the given lines by using vectors parallel to t...

A: Since you have asked multiple questions, we will solve the first question for you. If you want any s...

Q: Find a vector in the plane parallel to the line ax + by = c.

A: Given:

Q: The base of a solid is a circle with radius 5. Each cross section perpendicular to a fixed diameter ...

A: Given:The base of a solid is a circle with radius 5Then, the equation of the boundary of the circle ...

Q: For what number does the principal square root exceed eight times the number by the largest amount?

A: Given:The principal square root of a number exceeds eight times the number by the largest amount.

Q: Consider the series n-1 10" n=1 Determine whether the series converges, and if it converges, determi...

A:  We have the given series is of the form    

Q: Use the four-step process to find f' (x) and then find f'(1), f'(2), and f'(3). f(x) = x2 + 4x-4 f'(...

A:

Q: The heat experienced by a hiker at a campfire is proportional to the amount of wood on the fire and ...

A: Equation that relates heat intensity to amoumt of wood and distance is 

Q: Can you please explain and solve this using the concept of limits? Our topic right now is all about ...

A: Given : find the interval on which the following function is continuous.

Q: Find the volume V of the solid obtained by revolving about the line y = - 4 the region between the g...

A: Obtain the volume with the help of Washers method.

Q: Differentiation: definition and bas... Spanish oard | Khan Academy Differentiation: definition and b...

A: It is given that g be a function such that g (4) = 16.

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

A: Given:

Q: find the component form of the vector. The vector 2 units long in the direction 4i - j

A: Given vector is u = 4i – j. So, the unit vector in the direction of the given vector is

Q: Write an equation for the hyperbola with vertices at (-4,0), (4,0) and passing through (20,1).

A:

Q: Please solve and show your work

A: Given:

Q: What are quadric surfaces? Give examples of different kinds of ellipsoids, paraboloids, cones, and h...

A: Those equation or graph that can be represented in the below form are called Quadrative Surfaces:

Q: Show that except in degen-erate cases, (u * v) * w lies in the plane of u and v, whereas u * (v * w)...

A: Show that except in degenerate cases, (u x v) x w lies in the plane of u and v, whereas u x (v x w) ...

Q: Assume a quantity decreases by 5.1% in 7.5 hours.What is the half-life of the substance?

A: First of all, consider the formula for the decay of the substance and the half-life of the substance...

Q: A projectile is fired at a speed of 840 m/ sec at an angle of 60°. How long will it take to get 21 k...

A: Given:

Q: Can you please answer this question

A: Write tanx as sinx/cosx, then assume z=cosx and find dx. 

Q: Find a formula for the general term an of the sequence (starting with a1): {4/10,16/15,64/20,256/25,...

A: Given:

Q: Find a vector 5 units long in the direction opposite to the direction of v = (3/5)i + (4/5)k.

A: Given:

Q: What is special about the derivatives of vector functions of con-stant length? Give an example.

A: What is special about the derivatives of vector functions of constant length

Q: Evaluate the difference quotient for the given function. Simplify your answer. f(x) = x2 + 9,     ...

A: Given:

Q: Show that the center of the osculating circle for the parabola y = x2 at the point (a, a2) is locate...

A: We need to show that the centre of the osculating circle for the parabola y = x2 at the point (a, a2...

Q: Evaluate the surface integral. (4x + 4y + 4z)dS Where S is the parallelogram with parametric equatio...

A: To evaluate this integral, first change the variables to the parameters given in the surface as.

Q: Find the limit

A: Plug x=2 for the limit.

Q: Skill Practice 2 Solve the inequality. - 18x 2 3x2 - 4x3

A: Solving the inequality.

Q: In Exercises 1–3, find the curve’s unit tangent vector. Also, find the length of the indicated porti...

A: a) Find r’(t).

Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded b...

A: Given:

Q: Producers will make 4000 refrigerators available when the unit price is $290. At a unit price of $33...

A: Given:Producers will make 4000 refrigerators available when the unit price is $290. At a unit price ...

Q: Can I get help step by step with this problem please?

A: Given,

Q: Please solve and show your work

A: Given equation

Q: Show that dot multiplication of vectors is positive definite; that is, show that u.u>=0 for every...

A: Show that dot multiplication of vectors is positive definite; that is, show that u.u>=0 for every...

Q: A manufacturer has a monthly fixed cost of $36,000 and a production cost of $7 for each unit produce...

A: Part a)Formula for profit function: