Application of Derivatives (Tangent Line, Normal Line, Rate of Change)

Q: Given that u is a differentiable function, how do we get y' of y = arc csc(u)? T -^= f (x),n. (x),n.…

A: We can solve this as follows:

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: A series circuit has a resistance R = 10 Ohms and inductance L = 2. The battery gives a constant…

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Q: Find an equation of the level curve of the function z(x, y) = ey (x² + y2) that passes through the…

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A: Given s(t) = 2t3 - 92t2 - 40t + 3 let velocity function = v(t)

Q: Understand Properties of the Cross Product Find the Vector Orthogonal to Two Given Vectors Need a…

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Q: If x² + y² + z² = 9, dz dt = dx Š dt dy dt = 4, and = 3, find dz dt when (x, y, z) = (2, 2, 1).

A: x2+y2+z2=9 dxdt=4 and dydt=3 (x,y,z)=(2,2,1)   Differentiate the given function with respect to t:…

Q: Given the following differential equation: (y³+ kxy4 - 2x)dx + (3xy² + 20x² y³ - ky)dy = 0 a) Solve…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Find the average rate of change of f(x) = 4x² - 6 on the interval [1, a]. Your answer will be an…

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Q: The line normal to the graph of f at the point (1,2) passes through the point (-1,1).  Which of the…

A: Topic = Functions

Q: Find the slope of the tangent line (10-x)y² = x³ at the given point (5, 5). Round your answer to two…

A: Derivate the given equation with respect to x

Q: This is incorrect. Please resolve.. UPVOTE WILL BE GIVEN

A: The given answer is not incorrect it is just incomplete. Will be providing the complete solution in…

Q: Given that f(x) = x¹²h(x) h(-1) = 2 h'(-1)=5

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Q: Find Vectors and Perform Vector Operations in R³ Let a = (0, – 5, 5) and 6 = (4, 2, — 5). Find – 2ā…

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Q: Find the solution of 25+1 di +T=80e-0.04² Select one: O a. T = (3.2tc)e-0.04t O b. T = (3.2t + c)e…

A: Here we have to solve the differential equation.

Q: 2x+y=1" H...

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Q: Solve cosx dx + (sinx)y=1 Select one: O ay sinx + ccosx O b. y = 2sinx + 2cosx + c O c. y = sinx –…

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Q: Solve the initial value problem y" + 4y + 4y = 32e²; y(0)=-1, y'(0) = 14. +Set →→ (Answer: Y =…

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Q: 1. We are interested in evaluating the integral √ √9-² da. Note that this integral gives you the…

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Q: 2. An equation like sin2 ? + cos2 ? = 1 is an identity because it is true for all values of θ. If…

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Q: Find the critical numbers of the function f(x) = x5 - 5x¹ - 5x³+3 and classify them. Round your…

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Q: 3. Let f(t) = t(1 - 2t). a) Find the average rate of change of f(t) with respect to t as t changes…

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Q: In Exercises 13-16, find and sketch the level curves f(x, y) = c on the same set of coordinate axes…

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Q: CALCULUS

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Q: Find the derivative of the function: O y = a + (In²a + ln x + 1) O y = 2+1 ¹+¹(x ln² x + ln x + 1)…

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Q: Fxx is correct but Fxy is not 0.

A: The given function is f(x,y)=x4-5xy3+6y5 We have to find the fxx(x,y) and fxy(x,y)

Q: Find the derivative of the function: O y = e(ee+z) O y = e(e + 1) Oye (e + 1) Oy' = eªte²+et Y =…

A: eeex' =eeexeex' =eeexeex+x=eeex+ex+x

Q: e) y = √x4+7x

A: Solve for the derivative

Q: Find the general solution to the given equation 2y" + y − 3y = 0

A: The objective of the question is evaluate the given differential equations.

Q: Find the constant of integration for the DE dQ 2 + dr -Q=4; Q(2) = 100. 10+ 2r Select one: O a. 1306…

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Q: (b) Illustrate part (a) by graphing the curve and the tangent line on a common screen. (Graph the…

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Q: Find three positive numbers whose product is 117 such that the sum of their squares is as small as…

A: Let three positive numbers are x,y and z

Q: The

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Q: A person standing close to the edge on top of a 80-foot building throws a ball vertically upward.…

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Q: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:…

A: Let x m be  length and y m be  width of rectangle  Perimeter of rectangle=2x+y m Area of…

Q: (c) d (100K+200) ((-1)u) p (p)

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A: Yes, you are right there is some mistake in part e. so, I am rectifying it in next step. Sorry for…

Q: V-1 dv 32 = dt V e a) Write the given first-order LDE in standard form. b) Solve for the general…

A: Authoring guidelines: As per the authoring guidelines, we can solve only the first three parts of…

Q: Show that the triangle with vertices A, B, and C is a right triangle. d(A, B)2 = 145 d(A, C)² + d(B,…

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Q: Jse logarithmic differentiation to find the derivative of the f 3x y =(√x) ³x ''(x) =

A: We need to find out the differentiation of the function.

Q: B. At what rate the probability of de- veloping cancer increase with solar ex- posure

A: Given P(x)=e-2+x+3x21+e-2+x+3x2

Q: Find y' if 7 y² + sin (3x) = 12-y f

A: Here we can find the y' in the below steps, using implicit differentiation.

Q: Find equations of level curves containing a point Find an equation of the level curve of the…

A: Given fx, y=y2arctanx

Q: 1. Evaluate the integral f2162+12+0dx. (Hint. You may need to use partial fractions and trigono-…

A: Here we use the partial fraction to compute the integral . see below the answer and calculation we…

Q: Carl

A: Given - First 100 natural or counting numbers,  I.e.   n=. 1,2,3,4,5.......100. Required- Sum of…

Q: 19. a) Find an equation of the circle that satisfies the stated conditions. Center at the origin,…

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Q: Differentiate the function. g'(t) = g(t) = In t(t² + 1)8 3 4t 1 -

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Q: y = sec² x, y = 8 cos x || 5|3 DEIM 17373 ≤ x ≤ 3

A: Graph:-