Differentiation from first principles F(x)=x^4+1

Q: Evaluate the following integral using integration by parts. Sxe ³x d dx Use the integration by parts…

A: We have given to find integral  ∫xe3x dx Let,  I=∫x e3x dx Using integration by parts ∫u dv=uv-∫v du…

Q: 5.5 dy √y.evy 6. Š dx X+ e 7. fete d dx 8. fdx

A: Here we have to find the integral.

Q: if / 2³3 rsin rda -x³ cos x + 3x² sin x + 6x cos x Oxsin x O cos x sin x X COS X = 6 ƒ ƒ(x)dx, then…

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Q: Consider the function f(x) = r? – 5 +4 x + 1 a. Find the first derivative. f'(x) = b. List any…

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Q: The diagram shows three islands in a bay. You rent a boat and plan to visit each of these remote…

A: The diagram shows three islands in a bay. You rent a boat and plan to visit each of these remote…

Q: Find the solution to the differential equation that passes through the origin. z(t) = dz dt = 6te42

A: dzdt=6te4z⇒e-4zdz=6tdtIntegrating both sides we get,⇒zt=-ln-12t2-c14

Q: Prove the following, using the definition of a limit (convergence to a point). 3 n+2 lim 2- 004-u =…

A: We have given to prove  limn→∞2-3n+2=2 Taking left hand side of equation LHS = limn→∞2-3n+2 LHS =…

Q: Find the area of the surface generated when the given curve is revolved about the given axis. 5 9…

A: Use formula of area of surface generated about y axis

Q: D 5 yo

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Q: 27) Two points A and B are on opposite sides of a building. A surveyor selects a third point C to…

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Q: C. Domain Range D. Domain Range

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Q: 1 ) / ( ₁ + ²x^²) = ( -da f (₁ () [ dr. - 2³-1 2+1 (d) 2² + 7x+12² (a) +at da. dr.

A: Evaluate the integrals

Q: Find the area of the surface generated when the given curve is revolved about the given axis. y =…

A: The curve y=4x-6, for 52≤x≤92 rotated about y-axis we have to find the surface area of the solid

Q: 1₂ O 2² x² + x2° In | co - 3 2 O O None of the choices O +∞ dx In 2

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Q: Write the interval in set notation. [2, 6) {x | 2 < x ≤ 6} {x | 2 ≤ x < 6}   {x | 2 ≤ x ≤ 6} {x | 2…

A: Write the interval in set notation. [2, 6) {x | 2 &lt; x ≤ 6} {x | 2 ≤ x &lt; 6}   {x | 2 ≤ x ≤ 6}…

Q: If f(x) = 2x². -x-2 and g(x) = x + 2, then fog and go f may be expressed as f(g(x)) = ax + 3x +y and…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) 8 y = 2√x + 4 dx *- (√x +++1)x dy…

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Q: Evaluate the definite integral. Use a graphing utility to verify your result. 9 [(u - 2) du Submit…

A: Topic:- application of integration

Q: Find the velocity, acceleration, and speed of a particle with position function r(t) = (5 cos t,…

A: Given, r(t)=5 cos t, -3t, 5sin t

Q: 10. y = In(xtan y)

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Q: (2y + √y sin x) dx + xdy = 0

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Q: A water tower is located x = 275 ft from a building (see the figure). From a window in the building,…

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Q: 2 6) Compute the area bounded by y² + 2y + 4 and y = 4.

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Q: In March 2020, the PH coronavirus cases recorded was 2 089. By month of August 2020, the number of…

A: Here is the function we can use to calculate this. P= P° × e^rt Where p= population affected after…

Q: Use interval notation to determine f(x)

A: NOTE: Refresh your page if you can't see any equations. .

Q: An archeologist discovers a tool made of wood. The half- life of carbon-14 is approximately 5780…

A: Multiple sub-parts question-"As per our guidelines we are suppose to answer only first 3…

Q: 18. Create an equation and sketch the graph of a function using the following table: Time 0 15 30 45…

A: Given qiestion:- Create an equation and sketch the graph of a function using the following table:…

Q: 14) Using Newton's Method, find the zero for f(x)=-es-x+4,Xo = 2

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Q: Find the product z₁z₂ and the quotient Z1Z2 = N 11 Express your answers in polar form. Z2 Z₁ =…

A: We know that general property of trigonometry is - Cos(A+B ) = CosACosB - SinASinB. And Sin(A+B) =…

Q: Find the differential dy of the given function. (Use "dx" for dx.) 7 y = 6√x + dy = 3 x 1 1/2 x I 3…

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Q: 2 -1 4 3 N у -1 1 2 X

A: Graph of the function is given, we have to find its domain and range

Q: Use the law of sines to solve the triangle, if possible. B = 40°, C = 29°, b = 30 a = O A = (Do not…

A: The triangle has the measures B=40°, C=29°, b=30 Law of sines: sinAa=sinBb=sinCc

Q: Find the average value of the function over the given interval. (Round your answer to three decimal…

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Q: Use cylindrical coordinates to evaluate the integral below. F √x² + y²dv, where E is the region that…

A: We can solve this as follows:

Q: I need a step-by-step solution, please 2 bn=² ST T S™ sin x sin nx dx

A: To find out the integration given.

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE. Round your answer to four…

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Q: (2x² + 2xy + y²) dx + (x² + 2xy - y²) dy = 0

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Q: A. x(1 + y²) ź dx = y(1 + x²) z dy dy B. = x + y dx C. dx E. F. Which of the following are separable…

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Q: 9. (a) f(2) (b) f(1) 10. (a) f(-4) (1) f(-1) (c) (2) [y = f(x)] میر -2+ (b) f(0) (0) (4) v=fn

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Q: For the equation, find the slope m and y-intercept (0, b) (when they exist). (If an answer does not…

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Q: Evaluate the integral: J22 SVA-2 01- [] π [] +C dydz 4-2² e² +²

A: double integration using polar form

Q: Please, expert, Homework: Evaluate the following integrals 5.S√x+1d dx 4. nt to solve all these…

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Q: Find the derivative of x 1 f(x) = = 1₁² 1₁ ²² 16 dt S 1+t6 4 f'(x) =

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Q: the p 35) A building 240 feet tall casts a 30 foot long shadow. If a person stands at th shadow and…

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Q: 1 lim x cos- #48 X lim 00-00 = lim 20-00 cos (1/x) 1/x [-sin (1/x)] (1/2) -1/x² =lim sin 22-00 = 0 1…

A: Here, to evaluate limx→∞x cos1x

Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

A: Concept: Concavity: if f''(x)&gt;0 ∀ x∈R implies that f(x) is concave upward  And if f''(x)&lt;0 ∀…

Q: The derivative of f(x) = tan- is: Select one: O a. O b. O C. O d. 1 x² cos² 1 -1 x² cos² 1 xcos² 1 F…

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Q: ∞ 1.00 8e- dx = (If the integral diverges to ∞ or -∞, type oo or -oo; if the integral diverges in…

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Q: -4 -3 -2 -1 -5-4 5 4 3- 2+ 1 -Y -2+ -3+ -4+ -5+ 2 3 4 5 X

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Q: 5. Which of the following expresses √175 in simplest form ? a) 5√2 b) 5√7 c) 7√5 d) 9√5

A: Given that, the number is 175.