If the statement is true select true select true and write the proof on your notes. If the statement is false, select false and write a counter example. P: If n² + 131 is odd then also n +5 is also odd. a) True b) False

Q: The value of a car, V = f(a), in thousands of dollars, is a function of the age of the car, a, in…

A: Detailed solution of the problem is attached below.Explanation: Detailed explanation:

Q: d 3 Evaluate dx √√In(6 - x²) at x = 1.

A: −15ln(5)32​2​Explanation:

Q: 256x The volume of a sphere is increasing at a rate of 5 cm³/sec. Find the rate of change of its…

A: The volume of a sphere is increasing at a rate of 5 cm3/sec. To find the rate of change of its…

Q: 6) The region bounded by y= √x, y=2, x=0 is revolved about the x-axis to generate a solid, its…

A: The objective of this question is to find the volume of the solid generated when the region bounded…

Q: Use the Chain Rule to find the indicated partial derivatives. дл მs дл z = x² + x²y, x = s + 2t-u, y…

A: To express    dz/ds  , dz/dt and dz/du using the chain rule without substituting x and y: Apply the…

Q: Convert the Cartesian coordinate (-2,3) to polar coordinates, 0 ≤ 0 < 2π r = 0 =

A: r=(​13)θ=π−tan−123​Explanation:For any query with the solution, please ask in the comment box.

Q: f'(x) = ƒ' (e³) = f(x) = (ln x)7

A: ∙  f′(x)=x7(lnx)6​∙  f′(e3)=e35103​Explanation:

Q: 100 n=1 2

A:

Q: For the function f(x) = x^4 -6x^3+1, find the points of inflection.

A:

Q: Find all the values of x such that the given series would converge. n=1 (10x)" по The series is…

A:

Q: Consider the following. y= x²+27 54 y y=x³+27 x 3 (a) Write the integral that describes the area of…

A: (a)∫−30​(x3+27)dx(b)  4243​ square units Explanation:Step 1: Step 2:

Q: lim 2xy +5yz + 3xz (x,y,z) (0,0,0) 4x2 + 25y²+9z²

A: To find:-

Q: Use the Chain Rule to find dw/dt. dw dt = w = In x² + y² + z², x = 3 sint, y = 8 cost, z = 6 tan t

A: So, After the differentiation the final answer for the question is:…

Q: please solve  3[ln x - ln (x+9) - ln (x-9)]

A: The expression simplifies to:3ln(x2−81x​)Explanation:

Q: 6. Sketch an even continuous function with all of the following features: • Absolute minimum at -5 •…

A: Function is even continuous  function.  Absolute minimal at -5 Zeroes at 4 and -4y- intercept at -23…

Q: The function f(x) - 244 is concave down on which interval?

A: Given: To Find: To determine the interval on which the above function is concave down.

Q: 3. Use the method of shells to calculate the volume that is created when the following area is…

A: The exact volume is 92π(sin3−3cos3​ which is approximately equal to 2.17.Explanation:Steps and…

Q: Calculus 1 Question. Please help   Thank you

A: Ans : dxdy​=6cos6xExplanation:Explanation:

Q: Exercise: Solve the equation d²y dx² + y = tan x

A: The given differential equation is

Q: At time t, the position of a body moving along the s-axis is s=13-2112 +144t m. Find the body's…

A:

Q: what about the local minimum?

A: To find the point(s) of local minimum in the following graph.

Q: Solve the following initial value problem: with y(1) = 9. y = dy +8y = 1t

A:

Q: lim 47x cos(x)-47sin(x) Find the limit 0+x x sin²(x) lim x-0 47x cos(x)-47sin(x) x sin²(x)

A:

Q: Answer the following questions for the function defined on the interval [-15, 17]. 3 f(x) x = x² -…

A: a) Vertical Asymptotes   -4, 4 b) Concave Up  (−4,0)∪(4,17) c) Inflection point x-coordinate…

Q: Find the values of x, y and z that correspond to the critical point of the function: +5g f(x, y) =…

A: .

Q: Eliminate the parameter t to find a Cartesian equation in the form x = f(y) for: √x(t) = −3+² -…

A: Therefore, the required answer is x=16−3​y2+89​y−1627​Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Calculus I May I please have the solution for the following questions? Sketch an accurate graph…

A: Please refer below to get your solutions.Explanation:Sol -&gt; a) Sol -&gt; b) Sol -&gt; c) Sol…

Q: Is f(x)=2/x-7 one to one

A: The objective of this question is to determine whether the function f(x) = 2 / (x - 7) is…

Q: I need help with the plot. THANKS.

A: Answer is given below Explanation:

Q: If z = f(x, y), where f is differentiable, and x = g(t) y = h(t) h(1) = 5 h'(1) = -7 g(1) = 4 g'(1)…

A: Answer : -47Explanation:Note:f≡f(g(t),h(t))and   fx​≡fx​(g(t),h(t))

Q: nd the maximum rate of change of f(s, t) = test at the point (0, -3).

A:

Q: I need help with this problem and an explanation for the solution described below (Discrete…

A: The objective of the question is to find the negation of the given statement P: 'If all their…

Q: Evaluate the following integrals using partial fraction decomposition, when applicable

A: 26:To evaluate the integral ∫ dx/x^3−2x^2−4x+8​ using the partial fraction decomposition, we first…

Q: Find the equation of the tangent line at the indicated point. R(2)=log, (222-79), z=8

A: R(z)=log7⁡(2z2−79),z=8R′(z)=ddzlog7⁡(2z2−79)Using the Chain…

Q: Approximate 1714 using the Linear Approximation L(x) of f(x) = x 1/4 at a = 16. (Use symbolic…

A: The given function The linear approaximation at

Q: f(x, y, z) = √x + yz, P(1, 1, 3), u = (a) Find the gradient of f. Vf(x, y, z) = < (b) Evaluate the…

A: A) "&gt;&lt;2x+yz​1​,2x+yz​z​,2x+yz​y​&gt;B) "&gt;&lt;41​,43​,41​&gt;C)2815​Explanation:

Q: Direction: Please include your complete solution.

A: Question 1Slope=6x02​−6x0​Question 2The equation of the tangent line is y=2x+5. See explanation for…

Q: I do have the answer I just need the steps please

A: Answer in detailed belowm   In case of doubts please do ask in comments Explanation:Step 1:   Step…

Q: solve and include ristrictions for: In (In e (ext)) = 4 and 1 e X = 2

A:

Q: Evaluate the integral. π/2 0 [5 cos 17t i-4 sin 7t j + sin² 5t k] dt л/2 [5 cos 17t i-4 sin 7t j +…

A:

Q: Determine S f'(x) g(x) f(x) g'(x) dx (g(x))²

A:

Q: Evaluate the following surface integrals [ F. ds. (a) F(x, y, z) = (x, y, z) and S is the part of…

A: The solution is given below please refer to the solution  and if you have any doubt with regards to…

Q: principle: $15,000 Interest Rate: 12% Date borrowed:May 12 Date Repaid : September 16 Time:127…

A: The principal amount is P=15000The interest rate is r=12%=0.12Given time is t=127 days.The simple…

Q: Tutorial Exercise Find the arc length function for the curve y=2x3/2 with starting point Po(16,…

A:

Q: Differentiate the function. 이 y=(3x-2) (4-x)4 dy 口 dx

A: To differentiate the following function.

Q: y= log (ln 2x) (This function has no y intercept) • Is this function continuous ? Explain

A: Given function is log(ln2x).

Q: Question 2 The graphs of a function f and its derivative f' are shown. Identify each curve and…

A: We have graphs of f and f'We have to identify curve of f and f'

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS

A: The answers are as follows: (a) The vector equation of the plane is r.(−9,15,10)=−23. (b) The…

Q: Can you do part (b) ?

A: The solution is given below please refer to the solution  and if you have any doubt with regards to…

Q: 2. A rectangular bird sanctuary is being created with one side along a straight riverbank. The…

A: Let the length of the bird sanctuary  kmLet the width of the bird sanctuary  kmThe figure of the…