5. Find using first principles the slope of the tangent to f(x) = x² + 6x + 9 at x = -3.

Q: Problem 1. You are fencing in an area next to your house so your cats can lounge outside. The cat…

A: We have given the length of material that is avialble for fencing is 27 feet.

Q: Find the volume of the solid bounded by the elliptic paraboloid z = 1+ 2x² + 5y², the planes * = 5…

A:

Q: For the function f(x,y) = 8x² + 7y², find f(x + h,y)-f(x,y) = h f(x + h,y)-f(x,y) h

A: Given, f(x,y)=8x2+7y2

Q: What is the form of the particular solutiony for the P differential equation y" - y = R(x) where…

A:

Q: 3 Suppose ff(x) dx = 4 and f g (x) dx = 3. f(x and 19 (a) da = 3 1 3 Evaluate f (3 f (x) – 4 g(x))…

A:

Q: 1. Consider the vectors ā=27 +47-6k, b=-37+k, and a = 37-2k. [K/U] [1] a) Find the magnitude of the…

A:

Q: · (b + c) = a · = a · b + a · e for all a, b, c € R³. . 7. Prove that a.

A:

Q: B A 876, 5432 -10-9-8-7-6 -54 -3 -2 -1 1234 -1 Graph of f D 1 2 3 4 5 6 7 8 9 10 C x.

A: We will find the required.

Q: If a loading ramp is placed next to a truck, at a height of 8 feet, and the ramp is 22 feet long,…

A:

Q: Find a vector with initial point (4, -4,0) and terminal point (7, -14, - 10). Then find a unit…

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

Q: Evaluate the limit. Note: Enter two 'o's to make infinity (oo). 1 [ In(t-2) lim e³-t Check Answer

A: Given problem:- limt→∞4t,e3-t,1lnt-2

Q: In the below series find the missing noumber  2 , 3, 6, 11, 20, 37, 68, 125, 230, __ , 778,1431

A: Given data:- The below series is given, 2 , 3, 6, 11, 20, 37, 68, 125, 230, __ , 778,1431

Q: Evaluate the triple integral W z dV where E is the solid bounded by the cylinder y² + z² = 100 and…

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Q: Let à = (1, -2, 0) and 6 = (1, 3,2). b Find the angle between the vector (in radians) Check Answer

A:

Q: Solve the following first order differential equation: dy y² +49 +3 35 4 x² + 2x³-3x² dx == 0 given…

A: Differential equation: 35x4+2x3-3x2·dydx-y2+49x3=0

Q: Evaluate the integral by interpreting it in terms of areas. 4 to −9(1 − x) dx

A:

Q: A tank half-filled with water is in the form of a rectangular parallelepiped 5 ft deep, 15 ft wide,…

A:

Q: Using calculus, find the absolute maximum and absolute minimum of the function f(x) = 7x² − 14x + 4…

A:

Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

A: Given figure  with areas Now V=∫010f(x)dxV=∫03f(x)dx+∫35f(x)dx+∫57f(x)dx+∫710f(x)dx

Q: Sketch a graph of a continuous function f with the following properties: (i) f(x)=0 for x = 0 (ii)…

A:

Q: Solve the differential equation dy dx y²+7xy+16x² x² O a. x - y = O b. x + y 5 (y + 4x) In y O C. X…

A:

Q: Find the Taylor Series generated F(x) = ११० (7-X)12 {'(x) = (2x)10 9 (7-X)10 90 {"(x) = (7-x)" by…

A: To find the Taylor series generated by fx=17-x9 at x=6.

Q: Use L'Hopital rule, find the following limit? lim (4x + 1) cotx x→0+

A:

Q: 2. Let f(x, y) = |x − 1| · yś. (a) Compute, if they exist, the partial derivatives få and fy at the…

A:

Q: Determine the general solution of xdy + ydx = 0 A xy=c B) xy^2 = c y=c (D) X=C

A: Given Problem:- xdy+ydx=0 Find General equation  of given differential equation

Q: a) Use the Newton-Raphson method to solve the following equation for x to six decim x - ln x=8 (Use…

A: Here we have to use the Newton's raphson method

Q: Let r(t) = (-5t¹-2, - 5e³t, 2 sin(3t)) Find the unit tangent vector T (t) at the point t = 0. Round…

A: This question is related to differentiation, We will solve it using given information.

Q: For the function f(x)= −2sin(x−3π/2), determine its amplitude and period, and then graph it for two…

A:

Q: Find fxy(x,y) if f(x,y)= e 8xy² fxy(x,y)=

A:

Q: Find the limit. x²y lim (x,y) → (0,0) x² + 8y²

A: limx, y→0, 0x2yx2+8y2

Q: Suppose R is the solid bounded by the plane z = 5x, the surface z = x², and the planes y = 0 and y =…

A:

Q: 1. Which of the following relations is a function? a) {(1,9), (2, 4), (2, 3), (4, 15)} {(2, 7), (7,…

A: Recall:  A function can be defined as a relation between "each of its inputs" to "exactly one…

Q: (3x - 2y + 1) dx + (3x - 2y + 3) dy = 0.

A:

Q: Find the area under the curve y Т over the interval [1,4]

A: Topic = Area

Q: Find the curvature of the curve r(t) = (-1-4t, 2-t, 4 - 4t) at the point t = - 1. Check Answer

A: We know that curvature of a curve is given as: k=||r'(t)×r''(t)||||r'(t)||3

Q: 5. Which of the following functions grows the slowest as x goes to infinity? O 0.01x³ O 0.001x³…

A: We can solve this as follows:

Q: 10. Evaluate f(x) = 10-4x for f(3). a) 23 b) 2 c) 22 d) -2

A:

Q: Q7. Use Green's theorem to evaluate fy² dx + 3xy dy, where c is the boundary of the semi annular…

A:

Q: ¹ // x² + y² + 2² dV, where E is the ball: x² + y² + z² ≤ 16. Use spherical coordinates to evaluate…

A:

Q: √√√x- S: z 12, x² + y² ≤ 1 Evaluate (x - 2y + z) ds.

A:

Q: Find fxy(x,y) if f(x,y) = (x5 +y³) 7. fxy(x,y)=

A: Concept: Partial derivatives: In differential geometry and vector calculus, the partial derivative…

Q: fin(x² + 1)dx (Ans: xln(x² +1)−2x + 2 tan¯¹ x + C)

A:

Q: A body of mass 4 kg is projected vertically upward with an initial velocity 34 meters per second.…

A: Solution is given below:

Q: Consider the revenue function R(x) and cost function C(x) for a company, given by…

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Q: Given the following functions: y = For each function, sketch the curve and determine (where…

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Q: 1. Find the derivative function for the following using the power rule: a) f(x) = x¹² b) y = 8x³ -…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Find the average value of the following function where 9 ≤ x ≤ 11: f(x) = X C 81 dx

A:

Q: If u = sin® 3 - x 2 find Ou Əx Ou and ह Hence show that 2 Ou 1 y x 3 –x dy Ou = 0

A: Given u=sin-13-xy2

Q: Compute the given integral. fcos¹ a a sin ædx = +C

A: Our Aim is to evaluate the integral given below:-∫cos7 (x) sin (x) dx -(i)

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = ln(x + 5y + 6z). F(x, y, z) = =

A: