Using the definition, calculate the derivative of the function. Then find the values of the derivative as specified f(x)=7+x²; f'(-3), f'(0), f'(8) f(x)-

Q: iii) sin(xy)=x³ + x²y. Ex 2. Find the derivative dy for the following then evaluate the derivative…

A:

Q: Let f(x) = ex-x. (a) Find the critical values of f. Classify each of these values as a relative…

A: (a) Critical point x=0At, x=0 , f(x) has relative minimum value 1.(b) y=(e-1)x(c) a=0…

Q: What is the irrational number that is a particularly suitable base for both exponential and…

A: The irrational number that is particularly suitable as a base for both exponential and logarithmic…

Q: #1: For which of the cases below do the given functions form a fundamental set of solutions of the…

A: Summary: - (i) does not form a fundamental set due to missing different exponent solutions and…

Q: PLS HELP ON ALL ASKED QUESTIONS PLS

A: The point (1, 2, 3) is in the plane r=(−3,4,0)+t(6,4,−2)+s(1,−4,4).Explanation:Steps and…

Q: Find the limit, if it exists, or type 'DNE' if it does not exist.

A:

Q: For each function graphed below, state whether it is one-to-one. Graph 1 Graph 2 Graph 3 One-to-one?…

A: To find whether the given graph is one to one ?

Q: Find the first partial derivatives of the function 5x f(x, y) = (x + y)²° 1. fx(x, y) = 2. fy(x, y)…

A: 1.fx​(x,y)=(x+y)35y−5x​ 2.fy​(x,y)=(x+y)3−10x​Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Ex 1. Calculate the derivative i) x² + y² = 1. dy 33 dx for the following: ii) xy= x²+y.

A: To calculate the derivative  of the following.

Q: Please review and solve problem 8 part 'a' and 'b' and explain how the answer was found. Problem…

A: The answer is,Explanation:Consider,Used formulas:∫1 dx=x+C∫xn dx=n+1xn+1​+Crounded to six decimal…

Q: PLEASE ANSWER THE QUESTION ACCORDING TO INTERVAL NOTATION. AND PLEASE WRITE THE ANSWERS AT THE END…

A: a) (−23pi​,−2pi​)b) (0,0)c) (0.57,0.07904)d) (−6.18,−pi)∪(0,0.57).Explanation:a. Given the function…

Q: Solve the equation. 0.006x=25

A: x=536.48Explanation:Step 1: Take the logarithm of both sides lne0.006x=ln(25) Step 2: For the left…

Q: Q1/Show that the differential equation by by y' = x²y x³ + y³ is homogeneous and find the particular…

A:

Q: Find the arc length of the curve x = 3r², y = 4t³ on the interval 1≤t≤4. Round your answer to three…

A:

Q: PLS HELP ON ALL ASKED QUESTIONS PLS

A: Two planes intersect each other as the cross product of normal vectors is non-zero.Explanation:…

Q: f(x)= 3ex 2e-5

A: f(x)=3ex2ex−5f′(x)=ddx[3ex2ex−5]Using the quotient rule ddx[f(x)g(x)]=g(x)f′(x)−f(x)g′(x)[g(x)]2

Q: Evaluate √ x²ekx dx. (Helpful hint: √ ekx dx = €** + C) ekx k

A: To evaluate the following integral.

Q: 0218 X 17 (2) 600 x 38 131 784 X 44 (47664 X 18 157146X1

A: We need to perfrom multiplication.

Q: a. Use implicit differentiation to find dy dx b. Find the slope of the curve at the given point. 3…

A: 6xy=9(a)ddx(6xy)=ddx(9)Using the product ruleddx[f(x)g(x)]=f(x)g′(x)+g(x)f′(x)

Q: For the function g(x) graphed here, find the following limits or explain why they do not exist. a.…

A: The condition of existence of the limit at

Q: Find the critical value(s) and rejection region(s) for the indicated t-test, level of significance…

A: The objective of this question is to find the critical value and rejection region for a left-tailed…

Q: Find the volume of the solid generated by revolving the region bounded by the parabola y = and the…

A: To find the volume of the solid generated by revolving the region bounded by the parabola  and the…

Q: Solve the following logarithm equation then input your solution as an integer in the blank provided…

A: The equation:

Q: Compound Interest Match each formula for A with the correct name. Match each variable with its…

A: Compound interest formula: A = P(1+rt)Variable description:A: Final amountP: Principal amount…

Q: Q3/ Find the general solution of the differential equation dy 3x2 tan y)+ x³sec2y- = COS X dx 17.10.…

A:

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) 1-8 Inx;…

A: The objective of this question is to find the equation of the tangent line to the graph of the…

Q: Find the volume of the solid formed by revolving the region bounded by the graphs of y = 3 - x^2 and…

A: Given the region is bounded by the curve and line

Q: Is the point (1, 2, 3) on the plane = (-3,4,0)+(6,4,-2)+s(1,-4,4)? Show your work

A: The answer is given below Explanation:

Q: (Text' . | Find a ⋅ b if |a| = 5, |b| = 4, and the angle between a and b is radians. 8 • a b =

A: The formula for the dot product is : a⋅b = ∣a∣ ∣b∣ cos(θ)a⋅b  = 5* 4 *cos(π/8)a⋅b   = 18.4776…

Q: Determine the point of intersection between the following pair of lines (0, 1,3) + s(5,-1,2), SER…

A: The intersection point is (−5,2,1).Explanation:Steps and explanations are as follows:In case of any…

Q: Given the given cost function C(x)=8600+640x +0.5x² and the demand function p(x) 2 Find the…

A:

Q: To complete the process legible

A: The value of N is approximately 1.0895Explanation:Step 1:

Q: Find the derivative of the function. x+2x-2 y= 2 x-2x+2

A: y=x2+2x−2x2−2x+2y′=ddx(x2+2x−2x2−2x+2)Using the quotient…

Q: Fill in the blanks and evaluate the following indefinite integral. 2x dx = (x+4)2 -S dx = (x+4)2 x+4…

A:

Q: Hello Continuing with this problem, shown in the picture, where the parameterization for S was…

A: To calculate the surface area of S, we'll use the formula for the surface area of a parametric…

Q: ii) xy5/2+x³/2y 12. Point (4, 1). d²y Ex 3. Calculate the second derivative for the following: dx2…

A: The given equations are

Q: Find the first partial derivatives of f(x, y, z) = z arctan (1) at the point (1, 1, -5). af A. of…

A: A)25​B)−25​ C)4π​Explanation:

Q: Use the graph of the function f shown to estimate the indicated limits and the function value.…

A:

Q: ii) siny+x= y.

A:

Q: ƒ¹ ( x ) = {} (x² + x) (x² + x) * (2x + 1), determine a possible f(x). " If fi

A: The objective of the question is to find the function f(x) given its inverse function f inverse (x)…

Q: In order to find the derivative of f(x) = -x³ we use the power rule, which states that the…

A: The given function is

Q: (b) Find a particular solution of y"+9y+20y=6e-5x

A: Particular solution is  −6xe−5xExplanation:

Q: e exact area of the surface obtained by rotating the curve about the x-axis. 1 1 y = + ≤ X ≤ 1 6 2x…

A:

Q: Consider the following. y y=x³-2x -4 -2 + 2 2 y=2x 2 (a) Find the points of intersection of the…

A: Solution of the above mentioned problem is provided below for further queries u may ask in comments…

Q: I need help with this proble, a step by step breakdown in laymens terms. No hand written responses.

A: (A.)N′(x)=x23600​ (B.)N'(10) = 36Option B. At the $10,000 level of advertising, sales are increasing…

Q: pls help

A: Summary:- using basic mathematics Vector formulaExplanation:

Q: PLS HELP ON ALL ASKED QUESTIONS PLS

A: The answers are as follows: 7.The vector equation of the line isr=(7,2)+s(2,−3),s∈R.Option b. is…

Q: A man with $20,000 to invest decides to diversify his investments by placing $10,000 in an account…

A: The Data:We have two investments:Account 1: $10,000 at 5.2% compounded continuously (graphed as a…

Q: 2. Using the appropriate method taught in class solve the following questions. a) i. Find the…

A: Question No. (a):(i) To find the general solution of the following differential equation.(ii) To…

Q: Suppose a baby food company has determined that its total revenue R for its food is given by  R =…

A: A production level of 35 thousand units will maximize revenue.Explanation:To find the production…