Suppose f(x) is given.
Suppose point (a,b) is a point on the function f(x).
suppose line L1 is a tangent line to f(x) at point (a,b). Note: tangent line to a function is a line that touches the function at only one point.
1- What is the slope of the tangent line L1 described above (give an expression for the answer).
2- suppose slope of this tangent line L1 is m. What is equation of this tangent line (give an equation for the answer).
Want to see the full answer?
Check out a sample Q&A here
Related Calculus Q&A
Find answers to questions asked by students like you.
Q: Need help solving the equation that is attached
A: x->4^+ means x is slightly greater than 4. That means we have to use the part when x>4 to find...
Q: Optimization Problem A rectangle is constructed with its base on the diameter of a semicircle with r...
A: a)Let x and y be the base and height of the rectangle, respectively.Given that, the rectangle is con...
Q: The revenue from the sale of a product is, in dollars, R = 1500x + 3000(3x + 3)−1 − 1000 where x i...
A: The revenue from the sale of a product is, in dollars,R = 1500x + 3000(3x + 3)−1 − 1000where x is th...
Q: 2. Given the given function f(x) = x+defined on the interval [1, 3], determine if the function satis...
A: The given function is continuous and differentiable on the whole real numbers except zero. In partic...
Q: How can I get the result? Which is the result?
A: (a)we are given a function
Q: Use logarithmic differentiaion to evaluate f`(x) f(x) = (5x)^(ln 5x)
A: Click to see the answer
Q: what are the steps to solving |x-4| > 9
A: We have to solve the inequality.Inequality is given below:
Q: Find the function represented by the following series and find the interval of convergence of the se...
A: The function is given by,
Q: Suppose that the rate at which the concentration of a drug in the blood changes with respect to time...
A: Given:The rate of change of concentration of a drug in blood with respect to time t is
Q: How can I get the result? Which is the result?
A: The function is given as
Q: Which is the result?
A: We are given a function as
Q: Use Green's Theorem to evaluate the line integral oriented counterclockwise. Please refer to attach...
A: Given information:The circulation of the line integral of F=<3x^2, 6x^3+y>. where C be the bou...
Q: Please help. Find the values of x for which the given geometric series converges. Also, find the sum...
A: (a)Consider the given geometric series:
Q: Please help. Does the series below converge or diverge? Give a reason for your answer. (When checkin...
A: The given series is
Q: If the formula describing the distance s(in feet) an object travels as a function of time(in seconds...
A: The distance s(in feet) an object travels as a function is s = 100 + 160 t -16t2.It is known that, t...
Q: please explain how to do question 7c
A: The given integral is ∫(1-3x)4dx.
Q: suppose the line tangent to a graph of f at x = 4 is y = 3x+2 and suppose y = 5x -3 is the line tang...
A: Given information:The line tangent to a graph of f at x = 4 is y = 3x+2 and suppose y = 5x -3 is the...
Q: Differentiate xy^2+tan(y^3)=10y
A: Consider the given expression:
Q: The hyperbolic cosine function, denoted cosh x, is used to model the shape of a hanging cable (a tel...
A: Given information:Tyhe given function is cosh(x).
Q: 2x 1 dx 3 (2x-1+C 6 C 2 x2-x C 3x
A: Given:The integral is
Q: Let R be the region bounded by y x, x 1, and y 0. Use the shell method to find the volume of the sol...
A: (A)It is given that, the region bounded by y = x2, x = 1 and y = 0.The region around the line y = -8...
Q: c. Find the area of the reqion bounded by y xe-a and the x-axis on the interval 0,bl. Because this a...
A: Given curve is The area of the region bound by the curve and x-axis on the interval [0,b] is given b...
Q: Calculus Question
A: Let's call the given integral as I. Further let's make the substitution: x2 + 1 = zHence, 2xdx = dzP...
Q: Which of the following is the power series representation for f(x)? O A. B. 1 4k X Σ 4k k 0 1-x k 0 ...
A: Consider the power series representation for f(x4):
Q: Determine whether the alternating series converges or diverges
A: Check whether the series is convergent or divergent.
Q: Find the derivative of y with respect to x.
A: Assume z=x^5+1. Then found derivative dy/dx using the chain rule.
Q: I have trouble with second derivatives. I need help from my last step on please.
A: Given equations are,
Q: How can I get the result? Which is the result?
A: (a)Complete the table below analytically:
Q: y′=−3x+9 Determine the particular solution to the differential equation that passes through the poin...
A: The given differential equation is y’ = –3x+9.
Q: Find the average value of the function f(x) = e-4x on the interval [0, 1/2]. please show and expla...
A: The function is given by,
Q: a. find a possible function f and number a b. evaluate the limit by computing f`(a).
A: We first write the given function in the form of the definition of the derivative.
Q: Find f'(x) for f(x)=tan^3x+tan(x^3)
A: The function is given by,
Q: Determine the location and value of the absolute extreme values of f on the given interval, if they ...
A: Given infromation:The given funcion is
Q: Write the iterated integral for a sphere centered at (0,0,0) with a radius of 2. Use the order dz dx...
A: From the given the sphere equation is x2+y2+z2=22.
Q: How to convert percentage to ratio?
A: In this question we have to explain how to convert the percentage in fraction form.
Q: Is y=ex −5x−8 a solution to the initial value problem shown below? y′−5x=3+y y(0)=−7
A: The given differential equation is y=ex −5x−8.The solution of the deferential equation is given as, ...
Q: Do the domain of the following function:
A: Consider the provided function.
Q: :)
A: Given:The given curves are y = x2, x = 1, and y = 0.The volume of the solid revolved around the line...
Q: During the first 4 months of employment, the monthly sales S (in thousands of dollars) for a new sal...
A: During the first 4 months of employment, the monthly sales S (in thousands of dollars) for a new sal...
Q: Use a Maclaurin series in this table to obtain the Maclaurin series for the given function x2 In(1 x...
A: We know the Maclaurin series for ln(1+x). From there we find Maclaurin series for ln(1+x^3) by repla...
Q: PK P (K-P)e 8. Scientists use the Logistic Growth function P(t) = to model population growth where P...
A: The logistic growth function is given by,
Q: How can I get the result? Which is the result?
A: The given function is,
Q: Is y=e6x −3x−2 a solution to the differential equation shown below? y′−6y=7x+3
A: Here given differential equation is:Find the solution of given differential equation and match the g...
Q: Find the domain: g(x) = ln(e^x -5)
A: The domain of ln z is z>0. We'll use the same concept here. So e^x-5>0.
Q: 13. A 13 foot sliding ladder is leaning against a house when its base starts to slide away. By the t...
A: We are given diagram as
Q: How do I solve this differential equation using P(x), Q(x) and v(x)?
A: The given differential equation is,
Q: Find the aveage temperature in the box. Please refer to image. The bounds of x are 0 and ln3 The bo...
A: Given information:The given temperature distribution is T(x,y,z)=15e-x-y-z.
Q: Determine the location and value of extreme values of f on the given interval, if they exist. Type...
A: Given information:The given function is
Q: how to find Find the area of the region enclosed by one loop of the curve. r = sin(4θ)
A: The given curve is r= sin4thetaArea of the curve enclosed in the first loop is,
Q: Hello, I need help understanding how to form a general formula, using f(x)=5 tan x, for all the sol...
A: Consider the provided function.
