10. df f(x) = 3.² + 4x+ 2, find f(5) jccine The definition of derivative. f(5) is the limit. G5 X-7 the expression of The value * this limit is The this to find the equation of the langent line it to the parabela y + 3x² + 4x+2⁰ at the point (5,97) The equation of this targent line can the form y = L be written in day

Q: 2. If f(x) = √2 +4x, find f(3) of definition x → f'(3) using the , derivative. If" (3) is the limit…

A: Let's find value of f'(3) by using derivative of definition.

Q: 2. When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.01…

A: Given: Rate of increase of radius = 0.01 cm/min Radius = 50 cm

Q: V. Find the third derivative: 1) y = 10 tan(x) - 2 cot(x) 2) y = x³ - x² sin (x) 1 3) y = 2 sin(x)-4…

A: As per the guidelines I am supposed to do the first question among multiple questions. So here I am…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 6 - Lºcos…

A:

Q: z Find the Taylor polynomial på for f(x) = xe at z = 2.

A: we have to find the taylor polynomial P3   for function f(x)=xe-x  at  x =2   f(x) = xe-x   ⇒f(2)=…

Q: ind the Maclaurin Series for f(x) =1/(1+8x) and its interval of convergence.

A:

Q: Use Stokes' Theorem to evaluate SCF F. dr where C is oriented counterclockwise as viewed from above.…

A:

Q: Find the function y = ax²+bx+c whose graph contains the points (1,13), (-2,-8), and (2,28). What is…

A:

Q: The graph of a polynomial function f is shown below. -4 -3 a. The root(s) off with odd multiplicity…

A:

Q: 2x -5 dx x²-2x-8

A: I=∫2x-5x2-2x-8dx

Q: Find the following limits for f (x) lim f(x) = 0 x-4 If necessary, select the most informative…

A: Given query is to find indicated limit.

Q: Express the limit as a definite integral on the given interval. 2x;* + (x;*)² Ax, [1, 6] lim n→∞ dx

A:

Q: Find the gradient of the function g(x,y) = xy² at the point (2, -4). Then sketch the gradient…

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Q: Evaluate (6x +4√/y) ds where C is given in the accompanying figure. ...) 1- (0,0) y=x (1,1) y=x² X Q…

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Q: 1²2₂ f(x) dx where f(x) = 2 4x² if -2 ≤ x ≤0 if 0<x<2

A: We have to solve given Questions.

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A:

Q: Consider the following curve. ² = sin(28) Ф. Set up an integral that can be used to find the shaded…

A:

Q: Rewrite the expression f(x) = 8 x²+2x-3 using partial fractions. 1. f(x) 2. f(x) 3. f(x) = 5. f(x) =…

A: We have to find the partial fractions of the given equation.

Q: Convert the rectangular equation to an equation in cylindrical coordinates and spherical…

A:

Q: Solve the system by elimination: 4x - 3y-6z = 1 x-y-6z=5 6x - y = -11 Express your answer as an…

A: Given system of equations 4x - 3y -6z = 1 x - y - 6z = 5 6x - y = -11

Q: Use the definite integral to find the area between the x-axis and f(x) over the indicated interval.…

A:

Q: For the function below, find (a) the critical numbers; (b) the open intervals where the function is…

A:

Q: An arithmetic sequence has a15 = 86 and a34 = 200. Find a150. an = a₁ + (n − 1)d -

A: NOTE: Refresh your page if you can't see any equations. . it is given that

Q: ? Suppose flx) = 10 - x ² a) Find the slope of the tangent line to the graph yo fb) when x = 2 Slope…

A:

Q: Find the minimum distance from the point (-2, 2, -9) to the plane z - (4x + 3y) = 0. The minimum…

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Q: Let the angle theta = - 240 degrees. a) What quadrant contains theta? b) what is the corresponding…

A:

Q: For all of the following questions, assume x is in radians. a. Consider the function f(x) = sin(x).…

A: Given: y= sinx

Q: Differential Calculus Direction: Differentiate the following trigonometric functions: Part I. 1) y =…

A:

Q: The length of the arc of y = ln cos x from x = π/4 to x = π/3 equals______.

A:

Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) = 3t…

A: Given query is to find the displacement and total distance.

Q: Five years ago, you acquired a 30-year loan of $130,750, charging 6.8% annual interest, compounded…

A: We need to find amount for both cases.

Q: Determine all solutions to the equation 2sin² x = 1 + cos x on the interval [0, 2п). 0 О X= X= л 5л…

A:

Q: For f(x, y), find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously. f(x,…

A:

Q: 42. lim √√x = 0 0-x

A: Given query is to find the limit of the expression.

Q: B. Evaluate the following Laplace transforms by using the formulas listed in the table of Laplace…

A:

Q: Which of the following is equivalent to v = (-4, 3)?

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Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = t³i+ 4tj,…

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Q: Evaluate. Assume u> 0 when In u appears. 10) f(x5-2x4)4 (5x4-8x³) dx

A:

Q: 4. Determine if this function is continuous at x = 0. XW0 x=0 sin 5. Find a value of c so that f(x)…

A: Please see the below picture for detailed solution.

Q: Where on the interval [0, 7] is the secant line parallel to the tangent line for y = x sinx?

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Q: Identify any extrema of the function by recognizing its given form or its form after completing the…

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Q: What is the area bounded by y = 0, y = eˣ, x = 0 and x = 1?

A:

Q: 13. A right circular cylinder is inscribed inside a sphere with radius r = 3 inches. Find the…

A:

Q: dy dx - y = ex ; y(0) = −2

A: NOTE: Refresh your page if you can't see any equations. . compare this DE with   so here we have

Q: The function f(t) = 4(1.3) determines the height of a sunflower (in inches) in terms of the number…

A: Given function represents the height of a sunflower

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A: given  population start with 100 bees inceasing rate is  N(t)  bees per week

Q: (a) The series For the following answer blanks, decide whether the given sequence or series is…

A:

Q: How do you convert to cylindrical coordinates???

A: Given equation ( x2 + y2 )32  = 1  we want to convert the above equation in cylindrical coordinates…

Q: Suppose F′′(x)=Ax+B, with F′(1)=r and F(1)=s. Find F′(x) in terms of A, B, and r. F′(x)= Now find…

A:

Q: Determine whether each of the following vector fields F⃗ F→ is path independent (conservative) or…

A: use partial derivative for checking the path independent.