2. f(x) 3 cot (x T)+1 y PAGE 12 OF 13

Q: 0,-T <x<0 tsen x, 0sx < T 9. f(x) =

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Q: 7. The point of contact for a tangent to the curve f (x) = º is (2,4). It intersects the x and y…

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Q: 9. Find the constants a, b and c of cubic function f (x) = ax³ + bx + c such that : • The slope of…

A: Given that, f(x) = ax3 + bx  + c Slop of tangent line at x = 3 is 0. f'(1) = 24 f(x) croses the x…

Q: 2. a) Determine the coordinates of all point(s) on the graph of y = 2x In x where the tangent line…

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Q: 11.Determine the equation of the curve whose tangent line at any point (xy) is e* – sin x and passes…

A: Given problem:- Determine the equation of the curve whose tangent line at any point (x,y) is ex -sin…

Q: 4. Find the equation of the tangent line to f = 10** at x = 0. А. у %3D 1 B. x = 1 D. y = x – 1 E. y…

A: Tangent line equation =&gt;y – y1 = m (x – x1), where m is the slope and (x1, y1) is the coordinate…

Q: 4 sin x Let f(x) = 2 sin.x + 6 cos x Then f'(x) = The equation of the tangent line to y = f(x) at x…

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Q: 3. (a). For a curve defined by an equation f(x), satisfy dy + (1 – 2x)y = 4x for x > 0 and - dx f(1)…

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Q: 7) What is the equation of the tangent line of f(x) = xe"+ 3, at x = 0 a) Y= x+3 b) Y= 3 c) Y=…

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Q: r2x²+2x+1 Find the equation of the tangent line to the graph of F(x) = evy dy at x = 0. J sech x

A: We have to find the equation of the tangent line to the graph of F(x)=∫sechx2x2+2x+1eydy at x = 0.

Q: 6. Find the equation of the tangent line and the equation of the perpendicular line to the curves at…

A: By applying the applications  of derivative concepts we will find slope of the tangents to the…

Q: Q.3 Find dx dy by theorem and also check the results by implicit differentiation if x- 1 2y +xy = 0

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Q: (2 – 4t) sin() tan(2r) V17 – cos(2nt) Find the equation of the line tangent to the graph of f at r =…

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Q: 5. Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: The given parametric equations are, x=t3+cosπt, y=4t+sin2t+6. Find the equation of the tangent to…

Q: x +1 at (2,3) is x- 1 The equation of the tangent to the curve g(x) = 1) y = -2 2) y = 3x - 3 3) 2x…

A: To find the tangent to the curve

Q: (b) The tangent plane to the graph of z = f (x, y) at the point (1, 0, 1) can be described the…

A: We need to find the tangent plane to the graph of f(x,y)=e3yx4 at the point (1,0,1)

Q: 21 Find the value of c such that the line y = -x + is tangent to the curve y = c/x.

A: Given line ⇒y = 76x+212    .....(1)curve y = cx   ....(2)Differentiating w.r.t 'x'       (2)y' = c2x…

Q: 3. Find the slope of the tangent line to the curve y = +2 x*+4x+7 4. Determine and 4 of y = (5.x² –…

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Q: 1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula…

A: We will use chain rule of partial derivative  If F is a function of  two independent variables x and…

Q: 16. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is 3π 2 A.…

A: This is a basic application of derivative problem

Q: Can you help me step by step?

A: To determine the value of first and second derivative of the function

Q: Q1 If z is a differentiable function of x and y which satisfy equation x3 + y3 + 3 x? siny tan z = 5…

A: The detailed solution is as follows below:

Q: 4 sin x Let f(x) = 2 sin x + 4 cos e 4 Then f'(x) = (sin (z) + 2 cos (2)) The equation of the…

A: We are given,                 And we have found               . So, the slope of the tangent line…

Q: e equation of the tangent line to the curve y = . at the point (3,- ) ) is x+16y +11=0 x+8y - 7 = 0…

A: Topic:- calculus

Q: Find the equation of the tangent plane to z= e" +x+x³ +1 the point (2, 0, 12).

A: Let a surface be represented by the function fx, y, z = c where c is a constant. Then the equation…

Q: x² + 1 Find the tangent line of y = at r = 1

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Q: 5. Express the curve by an equation in x and y. x(t) = 2- sin(t) y(t) = cos(t) a. (x-2)² + y² =1 b.…

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Q: 1. Find the first derivative of y with respect to x (y') of the given functi 1. x³y-xy² +x² +y? = 0…

A: To find the first derivative of y using the given equation.

Q: The third derivative of y = cos 1 sin 27 1 111 a) y" b) y" 27 %3D 3 1 1 c) sin d) y 27 y = - %3D 27…

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Q: 20. What is the equation of the tangent line of f(x) = Vx = 4? A. x - 4y + 4 = 0 B. x + 4y -4 = 0…

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Q: 2 sin x Let f(x) 4 sin x + 6 cos x Then f' (x) = The equation of the tangent line to y = f(x) at a =…

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Q: 3n Find an equation of the tangent line to y = 7 sin(x) at x = .

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Q: 3) Find the slope of the curve defined by f (x) = x° sin x at x = T. 4) Differentiate g(x) = e* .

A: The slope of a curve y=f(x)  at a given point x=a is the value of dydx  at the given point x=a. So…

Q: 13. F(x) = sin t dt 20

A: We need to definite integral properties  also integral of sinx is -cosx

Q: Find an equation of the tangent line to the curve y = 4x sin (a) at the point (T /2,27). Express…

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Q: 5. Find G(1), G'(0), and G'(1/4), where G(x) = | tan t dt.

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Q: Find the maximum and minimum values of the function. (Round your answers to two decimal places.) y =…

A: Given query is to find the maximum and minimum value of the function for the interval.

Q: Find the absolute extrema of the function y tan( on the closed interval [0, 2]. %3D 8.

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Q: po Suppose h(x) = Vf(x) and the equation of the tangent line to f(x) at x = 1 is y = 4 + 1(x – 1).…

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Q: 3.9.27 Find the derivative of y with respect to x. y = sec 1(5x2 + 1). -1(5x2 +1), x > 0 dy %3D dx…

A: Please see the answer in Step 2

Q: Find the smallest positive c for which (c,0) is an x-intercept for the function f(x) = tan(1.46x).…

A: The given function is: f(x)=tan(1.46x) To find the smallest positive c for which (c,0) is an…

Q: 7 Find the value of c such that the line y =-x + 7 is tangent to the curve y = cyx. 4 с 3

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Q: 5. Find y' at the point (0, e) where xy² + In(x² + y) = 1.

A: Find y' = dy/dx At point (0, e)

Q: 11.Determine the equation of the curve whose tangent line at any point (x,y) is e* – sin x and…

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Q: 2. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is A. 2y +…

A: Equation of tangent line through A(x1 , y1) is given by :- y – y1 = slope x (x – x1)

Q: 11. Find an equation of the tangent to the curve y = In(4 + x") at the point %3D 12. i) Find the…

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Q: 3. Find the equation of the tangent line to the curve at (1,2) * y = 5 - x O A. x-6y + 22 = 0 O B.…

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Q: 9. Find the equation for the tangent line to f(x) = at *=-1 A)9x+25 y =-34 B)9x+25 y=-24 C)-9x+25y…

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

Q: Please solve the Vƒ of the function below at point P. a) f = (x² + y² + 2)-05, P; (12,0, 16) b) f =…

A: a) The given function is f=x2+y2+z2-0.5. This gives ∂f∂x=-0.5 x2+y2+z2-0.5-1…

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.