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Q: Find an equation of the tangent to the curve at the given point by both eliminating the parameter an...

A: First, to find equation of the tangent to the curve by without eliminating method:

Q: Find the linear approximation to the function. x2 f(x + Δx) ≈ Evaluate it at the given va...

A: Click to see the answer

Q: Find the partial derivatives, fx and fy, for f(x, y) = (5x + 4y)^10

A: f_x is partial derivative w.r.t. x. Used exponent rule and chain ruleAnswer: f_x= 50(5x+4y)^9

Q: 5 5 find sec(0) 12 and tan(e) 13 If sin(0)

A: Given,

Q: 7 If sin(0) 7 find sec(e) 24 and tan(0) 25

A: From the given information:

Q: The world's output of primary energy (petroleum, natural gas, coal, hydroelectricity, and nuclear el...

A: It is increasing at the rate of 2.4% annually. So 0.024 every year.growth rate= (1+0.024)=1.024 per ...

Q: For the composite function, identify an inside function and an outside function and write the deriva...

A: Given,

Q: I need help with question 39 in Section 4.1, page 284, of the James Stewart Calculus Eighth Edition ...

A: At first let us find the derivative of the function:

Q: Evaluate the expression without using a calculator. cos T 6 6 sin TT

A: From unit circle cos(pi/6)= sqrt(3)/2 sin(pi/6)=1/2

Q: There were 27 deer in a park on January 1, 2000. Six months later there were 38 deer in the same pa...

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for yo...

Q: Recall the arithmetic mean of two positive numbers a and b. Show that the value of c in the conclusi...

A: Consider the two positive number a and b and the function

Q: Assume that it costs a company approximately. C(x) = 400,000 + 160x + 0.003x2 dollars to manufac...

A: C'(x)= 160+.006xC'(10000)=160+.006(10000)=220Answer: The cost is increasing by $220 per smart phone ...

Q: Determine whether the geometric series is convergent or divergent. 10 − 4 + 1.6 − 0.64 + .... If...

A: Click to see the answer

Q: -32-9 9-4 2. Consider the following function f: r2 r< 1 f (x) = Find lim,1-f (x) (a) (b) Find lim,1+...

A: The given function is,

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

A: Hey, since there are multiple subparts posted, we will answer first three subparts. If you want any ...

Q: Problem 4: (a) Let f(x) = V+ x + 1 - Va4- 1. Show that f(x) = 0 has a solution. (b) Draw the graph o...

A: Since you have submitted two questions, we'll answer the first question. For the second question ple...

Q: Find the arc length of the following curve on the given integral by integrating with respect to x. f...

A: Consider the given curve.

Q: This is a 2 part question, kind of.... Part 1: Find the derivative.f (t) = 3t sin2 t Part 2: Is ther...

A: Given function is:Applying the derivative with respect to t and using the chain rule i.e. (uv)' = u'...

Q: Consider the following.x = sin(t)y = csc(t)0 < t < π/2(a) Eliminate the parameter to find a Ca...

A: It is given that,

Q: The length and width of a rectangle are measured as 89 cm and 22 cm, respectively. The error in meas...

A: According to the given information:Length of rectangle (l) = 89cmWidth of rectangle (b) = 22cmError ...

Q: Help please

A: To determine whether the given series is converges or diverges.Consider the function

Q: Suppose f(x, y) = ((xy2) / (x2 + y4)), for (x, y) ≠ (0, 0) ...

A: The given function is,

Q: A rectangle is constructed with its base on the x-axis and two of its vertices on the parabola y=16-...

A: Please see the white board. The rectangle is represented by the green line.The inverted parabola is ...

Q: Help for 2a,2b,2c.

A: Given,

Q: please answer question 19

A: Consider a function f(x)=2x+cosxWhen 2x+cosx=0 then f(x)=0f(x)=0 occurs at x intercept.

Q: Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing dev...

A: Refer to the question, we have to find the points on the curve where the tangent is horizontal or ve...

Q: Differentiate the function T(z) = 2z log2 z.

A: The given function is,

Q: Find the Taylor polynomial of degree 2 centered at (1, 2) for thefunction f(x, y) = 1/(xy)

A: Definition:

Q: Find the linearization L(z, y) of f at the given point. Surface: f(a, y) In(x +9y) Point: (11e5,e) F...

A: Given :

Q: Find the dimensions and volume of the right circular cylinder of maximum volume inscribed in a spher...

A: Let r be the radius of the cylinder and h be the height of the cylinderR is the radius of the sphere...

Q: Find a unit vector pointing in the direction in which the maximum rate of change occurs for the foll...

A: Click to see the answer

Q: Find the area of the surface generated when the curve f(x) = (2/3)x^(3/2) - (1/2)x^(1/2) ; [1,9] is ...

A: Given:

Q: Use the limit process to find the area of the region between the graph of the function and the x-axi...

A: Given:Use the limit process to find the area of the region between the graph of the function and the...

Q: The accompanying table gives the number of men 65 years or older in the United States and the percen...

A: Given the data

Q: 1. Find the following limits. e3r lim 3.x е (a) (b) lim e3/(2-a) lim In(1x2 - In(1 x (c) _ (d) lim l...

A: Click to see the answer

Q: Evaluate the difference quotient for the given function. Simplify your answer. f(x) = x2 + 5, ...

A: Substitute the values in difference quotient formula for x = (6+h) and x = 6. By the use of differen...

Q: Evaluate the integral dx/2sqr(x+3)+x

A: Given that

Q: Find the absolute maximum and the absolute minimum values of f on the given interval.

A: Calculate the derivative and equate it to zero to get the critical points,

Q: 4. Use the properties of logarith ms to rewrite each expression as the logarithm of a single express...

A: We know that,

Q: For the composite function, identify an inside function and an outside function and write the deriva...

A: The problem conerns applying chain rule by expressiong f(x) as a composite function f(x)=g(h(x)). We...

Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. 4. ...

A: We have to use area formula of polar coordinates with a= pi/2 and b=2pi

Q: Describe the motion of a particle with position (x, y) as t varies in the given interval.x = 3sin(t)...

A: To find: The motion of particle.The expression is rewritten as,

Q: Answer the following questions about the function whose derivative is f′(x)=(x+2)e^-x.Assume the do...

A: for increasing and decreasing the function.

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

A: It is given that the height of the pole is 60 ft and the ball is dropped from the height of 40 ft aw...

Q: lo eTTIoprvars ruc, -too 42 3r (c) Use the substitution rule to show that lim0 f(x) = lim^0+ f() and...

A: Given

Q: Please justify stuff that is asked. thank you have a wonderful day :)

A: Given function and point is

Q: Use the given parameters to answer the following questions. If you have a graphing device, graph the...

A: Click to see the answer

Q: Approximate the integral from 2 to 14 (x2 -5)dx using 4 rectangles

A: To find the area under the curve using rectangles, the Reimann sum is used.First, we need to find th...

Q: Find an equation of the line tangent to the curve defined by x^3+2xy+y^3=4 at the point (1,1).

A: To find the equation of the tangent line at the point (1, 1) to the curve given below.

Q: Find the intervals of increase or decrease. Find the local maximum and minimum values. Find the ...

A: Given: